train.jsonl

{"question": "Find x.", "answer": "3", "image_path": "train/0.png"}
{"question": "If $\\overline{B E} \\cong \\overline{E D}$ and $m \\widehat{E D}=120,$ find $m \\widehat{B E}$", "answer": "120", "image_path": "train/1.png"}
{"question": "Find x.", "answer": "2 \\sqrt { 221 }", "image_path": "train/2.png"}
{"question": "Find $x$ so that $m || n$.", "answer": "27", "image_path": "train/3.png"}
{"question": "GRID IN In the figure, the radius of circle $A$ is twice the radius of circle $B$ and four times the radius of circle $C .$ If the sum of the circumferences of the three circles is $42 \\pi,$ find the measure of $\\overline{A C}$", "answer": "27", "image_path": "train/4.png"}
{"question": "Find $m \\angle 2$.", "answer": "34", "image_path": "train/5.png"}
{"question": "Find the area of a regular hexagon with a perimeter of 72 feet.", "answer": "374.1", "image_path": "train/6.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "420", "image_path": "train/7.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth if necessary.", "answer": "108.5", "image_path": "train/8.png"}
{"question": "The triangle is inscribed into the circle. Find the exact circumference of the circle.", "answer": "12 \\pi", "image_path": "train/9.png"}
{"question": "Find x", "answer": "4", "image_path": "train/10.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth.", "answer": "311.5", "image_path": "train/11.png"}
{"question": "Find $x$ in the figure.", "answer": "16", "image_path": "train/12.png"}
{"question": "Find $x$.", "answer": "35", "image_path": "train/13.png"}
{"question": "In the figure, square $WXYZ$ is inscribed in $\\odot R$. Find the measure of a central angle.", "answer": "90", "image_path": "train/14.png"}
{"question": "Find y.", "answer": "45", "image_path": "train/15.png"}
{"question": "Find $\\angle D$ of quadrilateral ABCD", "answer": "45", "image_path": "train/16.png"}
{"question": "Find $x$.", "answer": "70", "image_path": "train/17.png"}
{"question": "The diagonals of rhombus FGHJ intersect at K. \r\nIf $m\\angle FJH = 82$, find $m\\angle KHJ$.", "answer": "49", "image_path": "train/18.png"}
{"question": "Find $y$ in the given parallelogram", "answer": "15", "image_path": "train/19.png"}
{"question": "Find $HK$.", "answer": "10", "image_path": "train/20.png"}
{"question": "$\\triangle RST \\cong \\triangle XYZ$. Find $y$.", "answer": "15", "image_path": "train/21.png"}
{"question": "Find x. Round to the nearest tenth.", "answer": "24.7", "image_path": "train/22.png"}
{"question": "Find DX if $E X=24$ and $D E=7$", "answer": "25", "image_path": "train/23.png"}
{"question": "Find $TR$.", "answer": "4", "image_path": "train/24.png"}
{"question": "Find z", "answer": "2 \\sqrt { 6 }", "image_path": "train/25.png"}
{"question": "Find the measure of $\\angle 4$ if $m∠4= m∠5$.", "answer": "32", "image_path": "train/26.png"}
{"question": "Find the perimeter of the triangle. Round to the nearest tenth if necessary.", "answer": "43.5", "image_path": "train/27.png"}
{"question": "If $\\overline{QR} \\| \\overline{XY}, XQ=15, QZ=12$, and $YR=20$, what is the length of $\\overline{RZ}$.", "answer": "16", "image_path": "train/28.png"}
{"question": "Find $x$.", "answer": "13.9", "image_path": "train/29.png"}
{"question": "In $\\odot P$, $PS=4$, find the length of $\\widehat {QR}$. Round to the nearest hundredth.", "answer": "4.75", "image_path": "train/30.png"}
{"question": "Find $y$ if $\\triangle JLM \\sim \\triangle QST$.", "answer": "4", "image_path": "train/31.png"}
{"question": "Find $MP$.", "answer": "8", "image_path": "train/32.png"}
{"question": "Find x.", "answer": "24 \\sqrt { 2 }", "image_path": "train/33.png"}
{"question": "For the pair of similar figures, use the given areas to find $x$.", "answer": "10.4", "image_path": "train/34.png"}
{"question": "Find the length of $\\widehat {ZY}$. Round to the nearest hundredth.", "answer": "5.24", "image_path": "train/35.png"}
{"question": "Find the value of x.", "answer": "130", "image_path": "train/36.png"}
{"question": "Find $m \\angle A B C$ if $m \\widehat{A B}=102$", "answer": "129", "image_path": "train/37.png"}
{"question": "If $R T=15, Q P=21,$ and $P T=8,$ find $T S$", "answer": "20", "image_path": "train/38.png"}
{"question": "$\\triangle K L N$ and $\\triangle L M N$ are isosceles and $m \\angle J K N=130$. Find the measure of $\\angle LKN$.", "answer": "81", "image_path": "train/39.png"}
{"question": "Find x. Round the side measure to the nearest tenth.", "answer": "34.8", "image_path": "train/40.png"}
{"question": "Find sinA", "answer": "\\sqrt { 26 } / 26", "image_path": "train/41.png"}
{"question": "If XM = 4, XN = 6, and NZ = 9, find XY.", "answer": "10", "image_path": "train/42.png"}
{"question": "Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "answer": "8", "image_path": "train/43.png"}
{"question": "Find $x$.", "answer": "\\frac { 26 } { 3 }", "image_path": "train/44.png"}
{"question": "In the figure, $m∠1 = 50$ and $m∠3 = 60$. Find the measure of $\\angle 2$.", "answer": "110", "image_path": "train/45.png"}
{"question": "Find the measure of $∠A$ to the nearest tenth.", "answer": "16.7", "image_path": "train/46.png"}
{"question": "Find x.", "answer": "2 \\sqrt { 13 }", "image_path": "train/47.png"}
{"question": "Find $ m ∠RSU $ so that $ m \\parallel n $.", "answer": "124", "image_path": "train/48.png"}
{"question": "Find tanB", "answer": "5", "image_path": "train/49.png"}
{"question": "$RP=3.5$ and $JP=9$. Find $PL$.", "answer": "7", "image_path": "train/50.png"}
{"question": "If PR || WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find SY", "answer": "4", "image_path": "train/51.png"}
{"question": "Find x.", "answer": "2 \\sqrt { 5 }", "image_path": "train/52.png"}
{"question": "The sum of the circumference of circles $H,J,K$ is $56 \\pi$ units. Find $KJ$.", "answer": "24", "image_path": "train/53.png"}
{"question": "Solve for x in the figure below.", "answer": "7", "image_path": "train/54.png"}
{"question": "Find the measure of $\\angle 2$ if $m \\angle D G F=53$ and $m \\angle A G C=40$.", "answer": "50", "image_path": "train/55.png"}
{"question": "Find $x$.", "answer": "4", "image_path": "train/56.png"}
{"question": "Find $m \\angle D G E$", "answer": "30", "image_path": "train/57.png"}
{"question": "Refer to the figure at the right. Find the value of $x$ if $ p \\parallel q $.", "answer": "45", "image_path": "train/58.png"}
{"question": "Find the length of $WY$", "answer": "9", "image_path": "train/59.png"}
{"question": "Find $m\\angle U$", "answer": "134", "image_path": "train/60.png"}
{"question": "$\\Delta DFG$  and $\\Delta F G H$ are isosceles, $m \\angle FDH=28$ and$\\overline{DG} \\cong \\overline{FG} \\cong \\overline{FH}$. Find the measure of $\\angle GFH$. ", "answer": "68", "image_path": "train/61.png"}
{"question": "Find y.", "answer": "1.5", "image_path": "train/62.png"}
{"question": "If $\\overline{PR} \\| \\overline{KL}, KN=9, LN=16,$ and $PM=2KP$, find $MN$.", "answer": "12", "image_path": "train/63.png"}
{"question": "Find $NP$.", "answer": "14", "image_path": "train/64.png"}
{"question": "In the figure, $ \\overline{JM} \\cong \\overline{PM}$ and $ \\overline{ML} \\cong \\overline{PL}$. If $m \\angle PLJ=34$, find $m \\angle JPM$.", "answer": "36.5", "image_path": "train/65.png"}
{"question": "Find $x$.", "answer": "12", "image_path": "train/66.png"}
{"question": "Find $x$.", "answer": "135", "image_path": "train/67.png"}
{"question": "If $\\overline{RQ} \\cong \\overline{RS}$ and $ m ∠RQS  = 75 $, find $ m ∠R $.", "answer": "30", "image_path": "train/68.png"}
{"question": "Find $y$ in the figure.", "answer": "40", "image_path": "train/69.png"}
{"question": "Find x to the nearest tenth.", "answer": "150", "image_path": "train/70.png"}
{"question": "Find $h$ in each triangle.", "answer": "6 \\sqrt 3", "image_path": "train/71.png"}
{"question": "Find x.", "answer": "10", "image_path": "train/72.png"}
{"question": "Find $x$.", "answer": "18", "image_path": "train/73.png"}
{"question": "Find x.", "answer": "\\frac { 4 } { 9 } \\sqrt { 3 }", "image_path": "train/74.png"}
{"question": "Trapezoid MNPQ has an area of 360 square feet. Find the length of $\\overline{MN}$.", "answer": "14", "image_path": "train/75.png"}
{"question": "Find x. Round side measures to the nearest tenth.", "answer": "15.1", "image_path": "train/76.png"}
{"question": "Each pair of polygons is similar. Find CD", "answer": "\\frac { 10 } { 3 }", "image_path": "train/77.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth.", "answer": "7.4", "image_path": "train/78.png"}
{"question": "If $\\frac{I J}{X J}=\\frac{HJ}{YJ}, m \\angle W X J=130$, and $m \\angle WZG=20,$ find $m \\angle JIH$", "answer": "50", "image_path": "train/79.png"}
{"question": "If $\\overline{W P}$ is a perpendicular bisector, $m \\angle WHA=8 q+17$, $m \\angle HWP=10+q$, $AP=6 r+4$, and $PH=22+3 r$, find $q$.", "answer": "7", "image_path": "train/80.png"}
{"question": "Find x", "answer": "5 \\sqrt { 3 }", "image_path": "train/81.png"}
{"question": "$a=14, b=48,$ and $c=50$ find $cosB$", "answer": "0.28", "image_path": "train/82.png"}
{"question": "Find $x$.", "answer": "9", "image_path": "train/83.png"}
{"question": "$\\triangle ABC$ is an isosceles triangle with base $BC$. What is the perimeter of the triangle?", "answer": "40", "image_path": "train/84.png"}
{"question": "$\\overline{XY}$ and $\\overline{XZ}$ are midsegments of $\\triangle RST$. Find $m \\angle RYX$.", "answer": "124", "image_path": "train/85.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "4", "image_path": "train/86.png"}
{"question": "Find the perimeter of trapezoid PQRS..", "answer": "38 + 6 \\sqrt { 2 } + 6 \\sqrt { 3 }", "image_path": "train/87.png"}
{"question": "Find $m\\angle 3$.", "answer": "99", "image_path": "train/88.png"}
{"question": "Find $m\\angle S$", "answer": "123", "image_path": "train/89.png"}
{"question": "Find x.", "answer": "4 \\sqrt { 3 }", "image_path": "train/90.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram.", "answer": "9", "image_path": "train/91.png"}
{"question": "Find $x$.", "answer": "107", "image_path": "train/92.png"}
{"question": "$m∠11 = 4x$, $m∠12 = 2x -6 $. Find the measure of $\\angle 12$.", "answer": "56", "image_path": "train/93.png"}
{"question": "Find $m \\angle TUV$", "answer": "53", "image_path": "train/94.png"}
{"question": "Find x", "answer": "6", "image_path": "train/95.png"}
{"question": "Find x", "answer": "4 \\sqrt { 6 }", "image_path": "train/96.png"}
{"question": "If $m\\angle BAD = 38$ and $m\\angle BCD = 50$, find $m\\angle ADC$.", "answer": "146", "image_path": "train/97.png"}
{"question": "Find $m \\angle 5$.", "answer": "110", "image_path": "train/98.png"}
{"question": "Find the perimeter or circumference of the figure. Round to the nearest tenth.", "answer": "25.1", "image_path": "train/99.png"}
{"question": "Find $x$ in the figure.", "answer": "90", "image_path": "train/100.png"}
{"question": "A square with side length of $9$ inches is inscribed in $\\odot J$. Find the exact circumference of $\\odot J$.", "answer": "9 \\sqrt 2 \\pi", "image_path": "train/101.png"}
{"question": "Find $x$.", "answer": "3", "image_path": "train/102.png"}
{"question": "If QRST is a parallelogram, find $x$", "answer": "5.4", "image_path": "train/103.png"}
{"question": "For trapezoid QRST, M and P are midpoints of the legs. If TS = 2x, PM = 20, and QR = 6x, find x.", "answer": "5", "image_path": "train/104.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "80", "image_path": "train/105.png"}
{"question": "Find x.", "answer": "14", "image_path": "train/106.png"}
{"question": "Find $m \\widehat {PO}$.", "answer": "112", "image_path": "train/107.png"}
{"question": "Find the perimeter of the triangle. Round to the nearest tenth if necessary.", "answer": "36", "image_path": "train/108.png"}
{"question": "Find $m\\angle D$", "answer": "117", "image_path": "train/109.png"}
{"question": "Points $P$, $Q$, and $R$ are the midpoints of $\\overline{J K}$, $\\overline{K L}$, and $\\overline{J L}$, respectively. Find $x$ .", "answer": "5.5", "image_path": "train/110.png"}
{"question": "Find $h$ in each triangle.", "answer": "\\frac { 15 \\sqrt 2 } { 2 }", "image_path": "train/111.png"}
{"question": "Find $XY$.", "answer": "7", "image_path": "train/112.png"}
{"question": "Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.", "answer": "4.1", "image_path": "train/113.png"}
{"question": "Find the scale factor from $W$ to $W'$.", "answer": "0.75", "image_path": "train/114.png"}
{"question": "Find $U B$ if $\\triangle R S T \\sim \\triangle U V W, \\overline{T A}$ and $\\overline{WB}$ are medians, $T A=8$, $R A=3, W B=3 x-6,$ and $U B=x+2$", "answer": "36", "image_path": "train/115.png"}
{"question": "$UJ=9, VJ=3$, and $ZT=18$. Find $JT$.", "answer": "6", "image_path": "train/116.png"}
{"question": "If $MNPQ \\sim XYZW,$ find the perimeter of $XYZW$.", "answer": "17", "image_path": "train/117.png"}
{"question": "Find the area of the figure.", "answer": "64", "image_path": "train/118.png"}
{"question": "Find x", "answer": "5 \\sqrt { 2 }", "image_path": "train/119.png"}
{"question": "Find $m \\angle 5$.", "answer": "85", "image_path": "train/120.png"}
{"question": "Quadrilateral $WXZY$ is a rhombus. If $m \\angle XZY=56$, find $m \\angle YWZ$.", "answer": "28", "image_path": "train/121.png"}
{"question": "Find the area of the figure in feet. Round to the nearest tenth, if necessary.", "answer": "14.4", "image_path": "train/122.png"}
{"question": "Find $x$.", "answer": "21", "image_path": "train/123.png"}
{"question": "In $\\odot P, P D=10, P Q=10,$ and $Q E=20$, find PE", "answer": "10 \\sqrt { 5 }", "image_path": "train/124.png"}
{"question": "If $WXYZ$ is a kite, find $ZY$.", "answer": "8 \\sqrt { 10 }", "image_path": "train/125.png"}
{"question": "Find the area of the regular polygon. Round to the nearest tenth.", "answer": "15.6", "image_path": "train/126.png"}
{"question": "If $m \\angle AFB = 8x - 6$ and $m \\angle BFC = 14x + 8$, find the value of $x$ so that $\\angle AFC$ is a right angle.", "answer": "4", "image_path": "train/127.png"}
{"question": "Find $x$.", "answer": "170", "image_path": "train/128.png"}
{"question": "Find $x$.", "answer": "11.2", "image_path": "train/129.png"}
{"question": "Find the area of the figure. Round to the nearest hundredth, if necessary.", "answer": "4", "image_path": "train/130.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "50", "image_path": "train/131.png"}
{"question": "Find x", "answer": "24", "image_path": "train/132.png"}
{"question": "Find x.", "answer": "\\frac { 13 \\sqrt { 2 } } { 2 }", "image_path": "train/133.png"}
{"question": "Find the measure of $\\angle 1$.", "answer": "56", "image_path": "train/134.png"}
{"question": "Find $y$.", "answer": "3", "image_path": "train/135.png"}
{"question": "Use parallelogram ABCD to find $m\\angle BCD$", "answer": "52", "image_path": "train/136.png"}
{"question": "In $\\odot A, m \\angle E A D=42$. Find $m \\widehat{C D}$", "answer": "138", "image_path": "train/137.png"}
{"question": "For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.", "answer": "\\frac { \\sqrt { 3 } } { 2 }", "image_path": "train/138.png"}
{"question": "Find x.", "answer": "4 \\sqrt { 13 }", "image_path": "train/139.png"}
{"question": "Find $x$. (Hint: Draw an auxiliary line.)", "answer": "130", "image_path": "train/140.png"}
{"question": "Find z", "answer": "2 \\sqrt { 6 }", "image_path": "train/141.png"}
{"question": "In $\\odot F$, find $m \\widehat {AED}$.", "answer": "153", "image_path": "train/142.png"}
{"question": "Find $y$ in the figure.", "answer": "26.3", "image_path": "train/143.png"}
{"question": "For trapezoid $ABCD$, $S$ and $T$ are midpoints of the legs. If $AB=3x$, $ST=15$, and $CD=9x$, find $x$.", "answer": "2.5", "image_path": "train/144.png"}
{"question": "If $BT = 5$ and $TC = 8$, find $CD$.", "answer": "\\sqrt { 89 }", "image_path": "train/145.png"}
{"question": "If $QR=2$, $XW=12$, $QW=15$, and $ST=5$, find $RS$.", "answer": "8", "image_path": "train/146.png"}
{"question": "In $\\odot W$, $\\widehat {RS} \\cong \\widehat {TV}$. Find $RS$.", "answer": "11", "image_path": "train/147.png"}
{"question": "In the figure, $m∠8 = 96$ and $m∠12 = 42$. Find the measure of $\\angle 9$.", "answer": "84", "image_path": "train/148.png"}
{"question": "$\\overline{JH}, \\overline{JP},$ and $\\overline{PH}$ are midsegments of $\\triangle KLM$. Find $x$.", "answer": "50", "image_path": "train/149.png"}
{"question": "Find y", "answer": "\\frac { 5 } { 3 }", "image_path": "train/150.png"}
{"question": "Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "14", "image_path": "train/151.png"}
{"question": "If $c=8,$ find $b$", "answer": "4 \\sqrt { 3 }", "image_path": "train/152.png"}
{"question": "Find $m\\angle T$", "answer": "58", "image_path": "train/153.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth.", "answer": "68.7", "image_path": "train/154.png"}
{"question": "Segments $\\overline{AD}$ and $\\overline{CE}$ are medians of $\\triangle ACB, \\overline{AD} \\perp \\overline{CE}, AB=10$, and $CE=9$. Find $CA$", "answer": "\\sqrt { 52 }", "image_path": "train/155.png"}
{"question": "In $\\triangle RST$, $Z$ is the centroid and $RZ=18$. Find $ZV$.", "answer": "9", "image_path": "train/156.png"}
{"question": "Find x.", "answer": "45", "image_path": "train/157.png"}
{"question": "In $\\odot B$, the diameter is 20 units long, and $m \\angle A C E=45$ Find $x$", "answer": "\\sqrt { 2 }", "image_path": "train/158.png"}
{"question": "Find $x$.", "answer": "145", "image_path": "train/159.png"}
{"question": "Find $m \\angle T$.", "answer": "135", "image_path": "train/160.png"}
{"question": "Find $x$.", "answer": "7", "image_path": "train/161.png"}
{"question": "In the figure, $m ∠ 12 = 64$. Find the measure of $ \\angle 5$.", "answer": "64", "image_path": "train/162.png"}
{"question": "Triangle $CDE$ has an area of 336 square inches. Find $CE$.", "answer": "28", "image_path": "train/163.png"}
{"question": "Find $x$ in the figure.", "answer": "16", "image_path": "train/164.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth.", "answer": "449.0", "image_path": "train/165.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "259.9", "image_path": "train/166.png"}
{"question": "Polygon ABCD ~ polygon AEFG, $m\\angle AGF = 108$, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26.\r\nFind the perimeter of trapezoid ABCD", "answer": "73.2", "image_path": "train/167.png"}
{"question": "In $\\odot B$, $m \\angle LBM = 3x$ and $m \\angle LBQ = 4x + 61$. What is the measure of $\\angle PBQ$?", "answer": "51", "image_path": "train/168.png"}
{"question": "Find x. Round the angle measure to the nearest degree.", "answer": "40", "image_path": "train/169.png"}
{"question": "Find $m \\angle 1$.", "answer": "108", "image_path": "train/170.png"}
{"question": "Find x", "answer": "22", "image_path": "train/171.png"}
{"question": "If $m\\angle ZYW = 2x - 7$ and $m \\angle WYX = 2x + 5$, find $m\\angle ZYW$.", "answer": "39", "image_path": "train/172.png"}
{"question": "Find $m\\angle B$", "answer": "90", "image_path": "train/173.png"}
{"question": "Find $x$ in each figure.", "answer": "31", "image_path": "train/174.png"}
{"question": "Find $m \\angle 6$.", "answer": "45", "image_path": "train/175.png"}
{"question": "Find x", "answer": "\\frac { 17 \\sqrt { 2 } } { 2 }", "image_path": "train/176.png"}
{"question": "If $FK = 3x - 1$, $KG = 4y + 3$, $JK = 6y - 2$, and $KH = 2x + 3$, find $x$ so that the quadrilateral is a parallelogram.", "answer": "4", "image_path": "train/177.png"}
{"question": "In $\\odot X, A B=30, C D=30,$ and $m \\widehat{C Z}=40$\r\nFind $m\\widehat{A B}$", "answer": "80", "image_path": "train/178.png"}
{"question": "Find $m \\angle Q$", "answer": "70", "image_path": "train/179.png"}
{"question": "Triangle $WXY$ has an area of 248 square inches. Find the length of the base.", "answer": "31", "image_path": "train/180.png"}
{"question": "Find $x$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "5.6", "image_path": "train/181.png"}
{"question": "Find $m \\angle 4$.", "answer": "125", "image_path": "train/182.png"}
{"question": "If WXYZ is a kite, find $YZ$", "answer": "\\sqrt { 89 }", "image_path": "train/183.png"}
{"question": "Find x. Round to the nearest tenth.", "answer": "5.2", "image_path": "train/184.png"}
{"question": "Find the measure of $\\angle B$", "answer": "46", "image_path": "train/185.png"}
{"question": "Find $m \\angle A G E$", "answer": "120", "image_path": "train/186.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "665.1", "image_path": "train/187.png"}
{"question": "$a=14, b=48,$ and $c=50$, find $tanB$", "answer": "3.43", "image_path": "train/188.png"}
{"question": "Find x", "answer": "22.5", "image_path": "train/189.png"}
{"question": "Find $x$.", "answer": "6", "image_path": "train/190.png"}
{"question": "Find $x$ so that the quadrilateral is a parallelogram", "answer": "11", "image_path": "train/191.png"}
{"question": "Use rhombus XYZW with $m \\angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\\frac{5 a+1}{4}$\r\nFind  XZ", "answer": "8", "image_path": "train/192.png"}
{"question": "Use rhombus XYZW with $m \\angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\\frac{5 a+1}{4}$\r\nFind  $m \\angle X Y W$", "answer": "53", "image_path": "train/193.png"}
{"question": "In the figure, $QR \\| TS$, $QT \\| RS$, and $m \\angle 1=131$. Find the measure of $\\angle 7$. ", "answer": "49", "image_path": "train/194.png"}
{"question": "Find x", "answer": "8 \\sqrt { 3 }", "image_path": "train/195.png"}
{"question": "Find $x$.", "answer": "25", "image_path": "train/196.png"}
{"question": "In the figure, $ \\triangle ABC$ is isosceles, $ \\triangle DCE$ is equilateral, and $ \\triangle FCG$ is isosceles. Find the measures of the $\\angle 3$ at vertex $C$.", "answer": "26", "image_path": "train/197.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "103.9", "image_path": "train/198.png"}
{"question": "Find y.", "answer": "\\frac { 3 } { 2 }", "image_path": "train/199.png"}
{"question": "Find $y$ and so that each quadrilateral is a parallelogram.", "answer": "\\frac { 4 } { 3 }", "image_path": "train/200.png"}
{"question": "In $\\triangle A B C, \\overline{B D}$ is a median. If $A D=3 x+5$ and $C D=5 x-1$, find  AC .", "answer": "28", "image_path": "train/201.png"}
{"question": "Find y", "answer": "32.6", "image_path": "train/202.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "261", "image_path": "train/203.png"}
{"question": "Find $m \\angle B$.", "answer": "30", "image_path": "train/204.png"}
{"question": "Find $m \\angle 2$.", "answer": "52", "image_path": "train/205.png"}
{"question": "The triangle is inscribed into the circle. Find the exact circumference of the circle.", "answer": "17 \\pi", "image_path": "train/206.png"}
{"question": "Find the area of the triangle. Round to the nearest tenth if necessary.", "answer": "137.5", "image_path": "train/207.png"}
{"question": "Use parallelogram MNPR to find $m \\angle MQN$", "answer": "97", "image_path": "train/208.png"}
{"question": "Find x.", "answer": "20 \\sqrt { 2 }", "image_path": "train/209.png"}
{"question": "If $a=4,$ find $b$", "answer": "4 \\sqrt { 3 }", "image_path": "train/210.png"}
{"question": "In the figure, $m ∠1 = 53$. Find the measure of $∠6$.", "answer": "53", "image_path": "train/211.png"}
{"question": "Find the area of the quadrilateral.", "answer": "240", "image_path": "train/212.png"}
{"question": "Find $JK$.", "answer": "14", "image_path": "train/213.png"}
{"question": "Find $AB$.", "answer": "29", "image_path": "train/214.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "145", "image_path": "train/215.png"}
{"question": "Find $x$.", "answer": "2", "image_path": "train/216.png"}
{"question": "Find $z$.", "answer": "20", "image_path": "train/217.png"}
{"question": "$\\overline{PM}$ is a diameter of $\\odot R$. Find $m \\widehat {MQ}$.", "answer": "65", "image_path": "train/218.png"}
{"question": "Find y.", "answer": "30", "image_path": "train/219.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "1448.0", "image_path": "train/220.png"}
{"question": "Assume that the segment is tangent, find the value of $x$.", "answer": "3", "image_path": "train/221.png"}
{"question": "Express the ratio of $ \\cos C $ as a decimal to the nearest hundredth.", "answer": "0.80", "image_path": "train/222.png"}
{"question": "Find the area of the triangle. Round to the nearest hundredth.", "answer": "6.79", "image_path": "train/223.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "38.4", "image_path": "train/224.png"}
{"question": "Find x.", "answer": "6", "image_path": "train/225.png"}
{"question": "If PR || WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find PQ", "answer": "6", "image_path": "train/226.png"}
{"question": "Find y", "answer": "\\frac { 19 \\sqrt { 2 } } { 2 }", "image_path": "train/227.png"}
{"question": "Find $x$ so that the quadrilateral is a parallelogram.", "answer": "8", "image_path": "train/228.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth.", "answer": "7.9", "image_path": "train/229.png"}
{"question": "If $ABCDE \\sim PQRST,$ find the perimeter of $PQRST$.", "answer": "22.5", "image_path": "train/230.png"}
{"question": "Find the value of the variable $x$ in the figure.", "answer": "70", "image_path": "train/231.png"}
{"question": "Each triangle in the figure is a $45^{\\circ}-45^{\\circ}-90^{\\circ}$ triangle. Find $x$.", "answer": "\\frac { 3 } { 2 }", "image_path": "train/232.png"}
{"question": "Find $m\\angle L$", "answer": "52", "image_path": "train/233.png"}
{"question": "The segment is tangent to the circle. Find $x$.", "answer": "20", "image_path": "train/234.png"}
{"question": "Find the area of the triangle. Round to the nearest tenth if necessary.", "answer": "20", "image_path": "train/235.png"}
{"question": "Find the area of the parallelogram.", "answer": "396", "image_path": "train/236.png"}
{"question": "Find $x$ in parallelogram $ABCD$.", "answer": "7.2", "image_path": "train/237.png"}
{"question": "If QRST is a parallelogram, Find $z$", "answer": "11", "image_path": "train/238.png"}
{"question": "Refer to the figure at the right. Find the value of $m ∠ ABD $ if $ p \\parallel q $.", "answer": "75", "image_path": "train/239.png"}
{"question": "Find $KL$.", "answer": "24", "image_path": "train/240.png"}
{"question": "In $\\odot D, \\overline{D E} \\cong \\overline{E C}, m \\widehat{C F}=60,$ and\r\n$\\overline{D E} \\perp \\overline{E C} .$ Find $m \\angle 5$", "answer": "30", "image_path": "train/241.png"}
{"question": "For trapezoid $D E G H, X$ and $Y$ are midpoints of the legs. Find $D E$", "answer": "8", "image_path": "train/242.png"}
{"question": "Point $S$ is the incenter of $\\triangle JPL$. Find $m \\angle MPQ$.", "answer": "56", "image_path": "train/243.png"}
{"question": "Find x.", "answer": "40", "image_path": "train/244.png"}
{"question": "Find $m \\angle 8$.", "answer": "28.5", "image_path": "train/245.png"}
{"question": "Find the height of the parallelogram given its area with 100 square units.", "answer": "5", "image_path": "train/246.png"}
{"question": "Find y", "answer": "16", "image_path": "train/247.png"}
{"question": "The height of a triangle is 5 centimeters more than its base. The area of the triangle is 52 square centimeters. Find the height.", "answer": "13", "image_path": "train/248.png"}
{"question": "Find the diameter of circle M.", "answer": "38.0", "image_path": "train/249.png"}
{"question": "Find $RT$.", "answer": "8", "image_path": "train/250.png"}
{"question": "Find $x$.", "answer": "20", "image_path": "train/251.png"}
{"question": "$\\overline{E C}$ and $\\overline{A B}$ are diameters of $\\odot O$.  Find its measure of $\\widehat{A C B}$. ", "answer": "180", "image_path": "train/252.png"}
{"question": "Use parallelogram $JKLM$ to find $m \\angle JML$.", "answer": "80", "image_path": "train/253.png"}
{"question": "Find $m\\angle C$", "answer": "127", "image_path": "train/254.png"}
{"question": "If QRST is a kite, find $m\\angle RST$.", "answer": "78", "image_path": "train/255.png"}
{"question": "In $\\odot P, m \\widehat{E N}=66$ and $m \\angle G P M=89$ . \r\nFind $m \\angle G M E$", "answer": "57", "image_path": "train/256.png"}
{"question": "Find $x$ if $AC=x-3$, $BE=20, AB=16,$ and $CD=x+5$", "answer": "35", "image_path": "train/257.png"}
{"question": "Find $ED$ if $AE=3, AB=2$, $BC=6,$ and $ED=2x-3$", "answer": "9", "image_path": "train/258.png"}
{"question": "Use a Pythagorean Triple to find x.", "answer": "34", "image_path": "train/259.png"}
{"question": "Find $x$.", "answer": "5", "image_path": "train/260.png"}
{"question": "Find EC", "answer": "4.8", "image_path": "train/261.png"}
{"question": "Find $m \\angle R$.", "answer": "32", "image_path": "train/262.png"}
{"question": "Find x.", "answer": "4 \\sqrt { 2 }", "image_path": "train/263.png"}
{"question": "Find x", "answer": "30", "image_path": "train/264.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "340", "image_path": "train/265.png"}
{"question": "Find the perimeter of the triangle.", "answer": "71.7", "image_path": "train/266.png"}
{"question": "Find the value of $x$ in the diagram.", "answer": "13", "image_path": "train/267.png"}
{"question": "$\\overline{AD}$ and $\\overline{CG}$ are diameters of $\\odot B$. Find $m \\widehat {CGD}$.", "answer": "305", "image_path": "train/268.png"}
{"question": "Lines $l$, $m$, and $n$ are perpendicular bisectors of $\\triangle PQR$ and meet at $T$. If $TQ = 2x$, $PT = 3y - 1$, and $TR = 8$, find $y$.", "answer": "3", "image_path": "train/269.png"}
{"question": "Find x", "answer": "44.9", "image_path": "train/270.png"}
{"question": "Find the measure of $\\angle 7$ if $\\overline{A B} \\perp \\overline{B C}$.", "answer": "140", "image_path": "train/271.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "53.4", "image_path": "train/272.png"}
{"question": "In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\\angle 6$.", "answer": "38", "image_path": "train/273.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "315", "image_path": "train/274.png"}
{"question": "Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "answer": "6", "image_path": "train/275.png"}
{"question": "Find y.", "answer": "3", "image_path": "train/276.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "46", "image_path": "train/277.png"}
{"question": "Find x.", "answer": "15", "image_path": "train/278.png"}
{"question": "Find $x$.", "answer": "50", "image_path": "train/279.png"}
{"question": "If $R T=16, Q P=24,$ and $S T=9,$ find $P S$", "answer": "13.5", "image_path": "train/280.png"}
{"question": "Find $CP$.", "answer": "8", "image_path": "train/281.png"}
{"question": "Circle $O$ has a radius of $10, A B=10$ and $m \\overrightarrow{A B}=60 .$ Find $m\\widehat{A Y}$", "answer": "30", "image_path": "train/282.png"}
{"question": "Let $\\overline{J K}$ be the median of $A B T Q .$ Find $J K$", "answer": "78", "image_path": "train/283.png"}
{"question": "Find the perimeter of each polygon for the given information.\r\n$B Y=C Z=A X=2.5$\r\ndiameter of $\\odot G=5$", "answer": "15 \\sqrt { 3 }", "image_path": "train/284.png"}
{"question": "In the figure, $a ∥ b, c ∥ d$, and $m∠4 = 57$. Find the measure of $\\angle 1$.", "answer": "123", "image_path": "train/285.png"}
{"question": "Find y", "answer": "30", "image_path": "train/286.png"}
{"question": "Find $m \\angle T$.", "answer": "55", "image_path": "train/287.png"}
{"question": "Find $m\\angle B$", "answer": "120", "image_path": "train/288.png"}
{"question": "Find $m \\angle 3$.", "answer": "51", "image_path": "train/289.png"}
{"question": "Find x.", "answer": "7 \\sqrt { 2 }", "image_path": "train/290.png"}
{"question": "Each pair of polygons is similar. Find y", "answer": "48.45", "image_path": "train/291.png"}
{"question": "Find $CD$ if $AB=6, AF=8, BC=x, CD=y$, $DE=2y-3,$ and $FE=x+\\frac{10}{3}$", "answer": "9", "image_path": "train/292.png"}
{"question": "Find the measure of $ \\angle 1$ in the figure.", "answer": "80", "image_path": "train/293.png"}
{"question": "Find $x$ so that the quadrilateral is a parallelogram", "answer": "3", "image_path": "train/294.png"}
{"question": "What is the area of the shaded region if $r=4$.", "answer": "64 - 16 \\pi", "image_path": "train/295.png"}
{"question": "Rhombus $RSTU$ has an area of 675 square meters. Find $SU$.", "answer": "45", "image_path": "train/296.png"}
{"question": "Use parallelogram $JKLM$ to find JK", "answer": "6", "image_path": "train/297.png"}
{"question": "Find x in the figure.", "answer": "16", "image_path": "train/298.png"}
{"question": "$\\overline{QS}$ is a diameter of $\\odot V$. Find $m \\widehat {STP}$.", "answer": "147", "image_path": "train/299.png"}
{"question": "Find the measure of $\\angle 1$.", "answer": "70", "image_path": "train/300.png"}
{"question": "Find $x$. $A = 78$ cm$^2$.", "answer": "8.0", "image_path": "train/301.png"}
{"question": "Find x.", "answer": "5 \\sqrt { 3 }", "image_path": "train/302.png"}
{"question": "Find $x$ so that the quadrilateral is a parallelogram", "answer": "2", "image_path": "train/303.png"}
{"question": "In $\\odot C$, $m \\angle HCG=2x$ and $m \\angle HCD=6x+28$, find $m \\widehat {HD}$.", "answer": "142", "image_path": "train/304.png"}
{"question": "In the figure, the vertices of quadrilateral ABCD intersect square EFGH and divide its sides into segments with measures that have a ratio of 1:2. Find the area of ABCD.", "answer": "45", "image_path": "train/305.png"}
{"question": "Find the measure of $XT$.", "answer": "7", "image_path": "train/306.png"}
{"question": "In $\\odot A, m \\angle E A D=42$. Find $m \\widehat{E D B}$", "answer": "222", "image_path": "train/307.png"}
{"question": "$m \\widehat{J H}=114$ Find $m\\angle 1$", "answer": "33", "image_path": "train/308.png"}
{"question": "Find the value of the variable w.", "answer": "8", "image_path": "train/309.png"}
{"question": "Find y.", "answer": "14", "image_path": "train/310.png"}
{"question": "Given $a ∥ b$, find $m∠1$.", "answer": "79", "image_path": "train/311.png"}
{"question": "In the figure, $ \\triangle ABC$ is isosceles, $ \\triangle DCE$ is equilateral, and $ \\triangle FCG$ is isosceles. Find the measures of the $\\angle 5$ at vertex $C$.", "answer": "18", "image_path": "train/312.png"}
{"question": "In $\\Delta G H J$, $H P=5 x-16$, $P J=3 x+8$, $m \\angle G J N=6 y-3$, $m \\angle N J H=4 y+23$ and $m \\angle H M G=4 z+14$. Find $m∠GJH$ if $\\overline{JN}$ is an angle bisector.", "answer": "150", "image_path": "train/313.png"}
{"question": "Find $x$.", "answer": "8", "image_path": "train/314.png"}
{"question": "Find $m \\angle A G D$", "answer": "90", "image_path": "train/315.png"}
{"question": "Find the measure of $∠T$ to the nearest tenth.", "answer": "64.6", "image_path": "train/316.png"}
{"question": "Find the perimeter of the triangle. Round to the nearest tenth if necessary.", "answer": "80", "image_path": "train/317.png"}
{"question": " In the figure, below, square $A B C D$ is attached to $\\triangle A D E$ as shown. If $m \\angle E A D$ is $30^{\\circ}$ and $A E$ is equal to $4 \\sqrt{3}$, then what is the area of square $A B C D $?", "answer": "64", "image_path": "train/318.png"}
{"question": "Find the area of the figure. Round to the nearest tenth.", "answer": "12", "image_path": "train/319.png"}
{"question": "Find $m \\angle 2$.", "answer": "39", "image_path": "train/320.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "153", "image_path": "train/321.png"}
{"question": "Find $m\\angle X$", "answer": "36", "image_path": "train/322.png"}
{"question": "Use rhombus $A B C D$ with $m \\angle 1=2 x+20, m \\angle 2=5 x-4$, $A C=15,$ and $m \\angle 3=y^{2}+26 .$ \r\nFind x", "answer": "8", "image_path": "train/323.png"}
{"question": "Find the area of the figure.", "answer": "150", "image_path": "train/324.png"}
{"question": "Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.", "answer": "4.1", "image_path": "train/325.png"}
{"question": "In the figure, $m ∠ 12 = 64$. Find the measure of $ \\angle 8$.", "answer": "116", "image_path": "train/326.png"}
{"question": "Each pair of polygons is similar. Find AB", "answer": "\\frac { 16 } { 3 }", "image_path": "train/327.png"}
{"question": "Find $y$.", "answer": "8", "image_path": "train/328.png"}
{"question": "The diameters of $\\odot A, \\odot B,$ and $\\odot C$ are $8$ inches, $18$ inches, and $11$ inches, respectively. Find $FB$.", "answer": "5", "image_path": "train/329.png"}
{"question": "Find y so that $e || f$.", "answer": "20", "image_path": "train/330.png"}
{"question": "In $\\odot G, m \\angle A G B=30$ and $\\overline{C G} \\perp \\overline{G D}$.\r\nFind $m \\widehat{B C D}$", "answer": "150", "image_path": "train/331.png"}
{"question": "In the figure, $m∠1 = 123$. Find the measure of $\\angle 11$.", "answer": "123", "image_path": "train/332.png"}
{"question": "MNQR is a rectangle. If $N R=2 x+10$ and $N P=2 x-30$\r\nfind $M P$", "answer": "40", "image_path": "train/333.png"}
{"question": "Find x. Round side measures to the nearest tenth.", "answer": "4.1", "image_path": "train/334.png"}
{"question": "Find the measure of the altitude drawn to the hypotenuse.", "answer": "\\sqrt { 26 }", "image_path": "train/335.png"}
{"question": "$\\overline{AD}$ and $\\overline{CG}$ are diameters of $\\odot B$. Find $m \\widehat {ACF}$.", "answer": "270", "image_path": "train/336.png"}
{"question": "Find $m \\angle ACB$.", "answer": "136", "image_path": "train/337.png"}
{"question": "Find y.", "answer": "3 \\sqrt { 13 }", "image_path": "train/338.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "39.4", "image_path": "train/339.png"}
{"question": "Find the measure of $\\angle 6$.", "answer": "140", "image_path": "train/340.png"}
{"question": "What is the value of x in the figure?", "answer": "26", "image_path": "train/341.png"}
{"question": "Refer to the figure at the right. The orthocenter of $\\triangle A B C$ is located 6.4 units from point $D$. Find $B C$.", "answer": "10.03", "image_path": "train/342.png"}
{"question": "If $EN=13$, what is the diameter of the circle?", "answer": "26", "image_path": "train/343.png"}
{"question": "In the figure, $m ∠ 12 = 64$. Find the measure of $ \\angle 3$.", "answer": "116", "image_path": "train/344.png"}
{"question": "Find the area of the trapezoid.", "answer": "272", "image_path": "train/345.png"}
{"question": "In right triangle $ABC$ shown below, what is the measure of $∠ A$ to the nearest tenth of a degree?", "answer": "38.9", "image_path": "train/346.png"}
{"question": "Find x. Assume that any segment that appears to be tangent is tangent.", "answer": "9", "image_path": "train/347.png"}
{"question": "Use rhombus XYZW with $m \\angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\\frac{5 a+1}{4}$\r\nFind  XW", "answer": "5", "image_path": "train/348.png"}
{"question": "In $\\odot G, m \\angle A G B=30$ and $\\overline{C G} \\perp \\overline{G D}$.\r\nFind $m \\widehat{A B}$", "answer": "30", "image_path": "train/349.png"}
{"question": "Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "5", "image_path": "train/350.png"}
{"question": "Find z", "answer": "25", "image_path": "train/351.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "54", "image_path": "train/352.png"}
{"question": "Find x", "answer": "18", "image_path": "train/353.png"}
{"question": "Find x", "answer": "6", "image_path": "train/354.png"}
{"question": "Quadrilateral $ABCD$ is a rhombus.  If $m\\angle DPC = 3x – 15$, find $x$.", "answer": "35", "image_path": "train/355.png"}
{"question": "$∠6$ and $∠8$ are complementary, $m∠8 = 47$. Find the measure of $\\angle 6$.", "answer": "43", "image_path": "train/356.png"}
{"question": "Find $m \\angle K$.", "answer": "117", "image_path": "train/357.png"}
{"question": "Find $y$ if $m∠5 = 68$ and $m∠3 = 3y - 2$.", "answer": "38", "image_path": "train/358.png"}
{"question": "Find x so that $GJ \\parallel FK$. GF = 12, HG = 6, HJ = 8, JK = x - 4.\r\n", "answer": "20", "image_path": "train/359.png"}
{"question": "Find $m \\widehat{E D B}$ if $m \\widehat{F E}=118, m \\widehat{A B}=108$, $m \\angle E G B=52,$ and $m \\angle E F B=30$.", "answer": "15", "image_path": "train/360.png"}
{"question": "Find $m\\angle R$", "answer": "150", "image_path": "train/361.png"}
{"question": "$\\ln \\odot K$, $ M N=16$ and $m \\widehat{M N}=98$. Find the measure of $m \\widehat{NJ}$. Round to the nearest hundredth.", "answer": "131.00", "image_path": "train/362.png"}
{"question": "Find the perimeter of $\\triangle C B H,$ if $\\triangle C B H \\sim \\triangle F E H, A D E G$ is a parallelogram, $C H=7, F H=10$, $F E=11,$ and $E H=6$.", "answer": "18.9", "image_path": "train/363.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "9", "image_path": "train/364.png"}
{"question": "$m \\angle 2=2 x, m \\angle 3=x$ Find $m\\angle 1$", "answer": "30", "image_path": "train/365.png"}
{"question": "If $\\overline{PR} \\| \\overline{KL}, KN=9, LN=16,$ and $PM=2KP$, find $ML$.", "answer": "20", "image_path": "train/366.png"}
{"question": "Find $SW$.", "answer": "16", "image_path": "train/367.png"}
{"question": "$\\overline{GJ}$ is a diameter of $\\odot K$. Find $m \\widehat {GLH}$.", "answer": "238", "image_path": "train/368.png"}
{"question": "If $ABCD$ is a kite, Find $m \\angle C$", "answer": "70", "image_path": "train/369.png"}
{"question": "Find the perimeter of the triangle. Round to the nearest tenth if necessary.", "answer": "13.2", "image_path": "train/370.png"}
{"question": "Triangle RST is circumscribed about the circle below. What is the perimeter of the triangle?\r\n ", "answer": "36", "image_path": "train/371.png"}
{"question": "Find $m \\angle PQS$.", "answer": "42", "image_path": "train/372.png"}
{"question": "Find x. Round to the nearest tenth if necessary.", "answer": "2", "image_path": "train/373.png"}
{"question": "Find $x$ in the figure.", "answer": "34", "image_path": "train/374.png"}
{"question": "Find y in the parallelogram", "answer": "8", "image_path": "train/375.png"}
{"question": "Find the variable of $b$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "11.3", "image_path": "train/376.png"}
{"question": "Find y.", "answer": "15", "image_path": "train/377.png"}
{"question": "Find x.", "answer": "4 \\sqrt { 3 }", "image_path": "train/378.png"}
{"question": "Find the area of the triangle. Round to the nearest hundredth.", "answer": "23.39", "image_path": "train/379.png"}
{"question": "Find the perimeter of $▱ ABCD$.", "answer": "28", "image_path": "train/380.png"}
{"question": "Solve for x in the figure.", "answer": "4", "image_path": "train/381.png"}
{"question": "In the figure, $m∠3 = 110$ and $m ∠ 12 = 55$. Find the measure of $∠15$.", "answer": "55", "image_path": "train/382.png"}
{"question": "In the figure, $m ∠1 = 58 $, $m ∠2 = 47 $, and $m ∠3 = 26 $. Find the measure of $∠7$.", "answer": "58", "image_path": "train/383.png"}
{"question": "For trapezoid QRST, M and P are midpoints of the legs. If TS = 2x + 2, QR = 5x + 3, and PM = 13, find TS.", "answer": "8", "image_path": "train/384.png"}
{"question": "Find the measure of $\\angle R$", "answer": "122", "image_path": "train/385.png"}
{"question": "Find the circumference of $\\odot S$. Round to the nearest hundredth.", "answer": "40.83", "image_path": "train/386.png"}
{"question": "Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.", "answer": "168.2", "image_path": "train/387.png"}
{"question": "$\\overline{AD}$ and $\\overline{CG}$ are diameters of $\\odot B$. Find $m \\widehat {GCF}$.", "answer": "325", "image_path": "train/388.png"}
{"question": "Find the measure of $\\angle 3$.", "answer": "49", "image_path": "train/389.png"}
{"question": "Find $JK$.", "answer": "24", "image_path": "train/390.png"}
{"question": "In the figure, $m∠4 = 104$, $m∠14 = 118$. Find the measure of $\\angle 7$.", "answer": "76", "image_path": "train/391.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "13", "image_path": "train/392.png"}
{"question": "Find $x$.", "answer": "71", "image_path": "train/393.png"}
{"question": "Find x.", "answer": "\\frac { 15 } { 2 } \\sqrt { 3 }", "image_path": "train/394.png"}
{"question": "$\\overline{QS}$ is a diameter of $\\odot V$. Find $m \\widehat {QRT}$.", "answer": "255", "image_path": "train/395.png"}
{"question": "Find $BC$.", "answer": "10", "image_path": "train/396.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "18", "image_path": "train/397.png"}
{"question": "Find the measure of $\\angle 1$ if $m∠DGF = 53$ and $m∠AGC = 40$.", "answer": "37", "image_path": "train/398.png"}
{"question": "Find $KL$.", "answer": "14", "image_path": "train/399.png"}
{"question": "Find $x$.", "answer": "48", "image_path": "train/400.png"}
{"question": "$\\triangle K L N$ and $\\triangle L M N$ are isosceles and $m \\angle J K N=130$. Find the measure of $\\angle LNM$.", "answer": "20", "image_path": "train/401.png"}
{"question": "Find $x$.", "answer": "7", "image_path": "train/402.png"}
{"question": "Find x", "answer": "14 \\sqrt { 3 }", "image_path": "train/403.png"}
{"question": "$P Q R S$ is a rhombus inscribed in a circle. Find $m \\angle Q R P$ ", "answer": "45", "image_path": "train/404.png"}
{"question": "Find y.", "answer": "\\frac { 15 } { 2 }", "image_path": "train/405.png"}
{"question": "ABCD is a rhombus. If EB = 9, AB = 12 and $m\\angle ABD = 55$ . Find $m\\angle ACB$", "answer": "35", "image_path": "train/406.png"}
{"question": "Find y. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth if necessary.", "answer": "12.6", "image_path": "train/407.png"}
{"question": "Use parallelogram JKLM to find b if $J K=2 b+3$ and $J M=3 a$.", "answer": "21", "image_path": "train/408.png"}
{"question": "According to the Perpendicular Bisector Theorem, what is the length of segment AB below?", "answer": "2.5", "image_path": "train/409.png"}
{"question": "Find x. Round side measures to the nearest tenth.", "answer": "8.1", "image_path": "train/410.png"}
{"question": "Find $x$.", "answer": "8", "image_path": "train/411.png"}
{"question": "Find $x$.", "answer": "93", "image_path": "train/412.png"}
{"question": "Find $m\\angle C$", "answer": "120", "image_path": "train/413.png"}
{"question": "Find $x$ so that $p ∥ q$.", "answer": "9", "image_path": "train/414.png"}
{"question": "Find $m \\angle 1$.", "answer": "62", "image_path": "train/415.png"}
{"question": "$A B C D$ is a rectangle. If $A C=30-x$ and $B D=4 x-60$\r\nfind $x$", "answer": "18", "image_path": "train/416.png"}
{"question": "Find x in the figure.", "answer": "31", "image_path": "train/417.png"}
{"question": "Find x.", "answer": "2 \\sqrt { 10 }", "image_path": "train/418.png"}
{"question": "Express the ratio of $\\sin A$ as a decimal to the nearest hundredth.", "answer": "0.38", "image_path": "train/419.png"}
{"question": "Find $x$ so that $p \\parallel q$.", "answer": "44", "image_path": "train/420.png"}
{"question": "Express the ratio of $\\tan Q$ as a decimal to the nearest hundredth.", "answer": "0.53", "image_path": "train/421.png"}
{"question": "If $J L=27, B L=9,$ and $J K=18,$ find $J A$.", "answer": "12", "image_path": "train/422.png"}
{"question": "Find $m\\angle Z X V$", "answer": "115", "image_path": "train/423.png"}
{"question": "Find $m\\angle G$", "answer": "107", "image_path": "train/424.png"}
{"question": "If $x=7 \\sqrt{3},$ find $a$", "answer": "14 \\sqrt { 3 }", "image_path": "train/425.png"}
{"question": "Find the area of the kite.", "answer": "178.5", "image_path": "train/426.png"}
{"question": "Find $MN$.", "answer": "29", "image_path": "train/427.png"}
{"question": "In the figure, $m∠3 = 43$. Find the measure of $\\angle 7$.", "answer": "43", "image_path": "train/428.png"}
{"question": "Find x.", "answer": "32.2", "image_path": "train/429.png"}
{"question": "Find the area of the triangle. Round to the nearest hundredth.", "answer": "0.92", "image_path": "train/430.png"}
{"question": "For the pair of similar figures, use the given areas to find $x$.", "answer": "20.0", "image_path": "train/431.png"}
{"question": "In the figure, $m ∠9 = 75$. Find the measure of $\\angle 3$.", "answer": "75", "image_path": "train/432.png"}
{"question": "$P$ is the incenter of $\\triangle AEC$. Find $m \\angle DAC$.", "answer": "33", "image_path": "train/433.png"}
{"question": "If KLMN is a parallelogram, find the value of the indicated variable. \r\nFind x", "answer": "4", "image_path": "train/434.png"}
{"question": "Find $m \\angle P$.", "answer": "70", "image_path": "train/435.png"}
{"question": "If $QV=8$, what it the diameter of $\\odot Q$.", "answer": "16", "image_path": "train/436.png"}
{"question": "Find the area of the figure.", "answer": "77", "image_path": "train/437.png"}
{"question": "Find x.", "answer": "5", "image_path": "train/438.png"}
{"question": "Points $S$, $T$, and $U$ are the midpoints of $\\overline{DE}$, $\\overline{EF}$, and $\\overline{DF}$, respectively. Find $y$.", "answer": "5.8", "image_path": "train/439.png"}
{"question": "Find the area of the kite.", "answer": "137.5", "image_path": "train/440.png"}
{"question": "Find x to the nearest hundredth.", "answer": "8.39", "image_path": "train/441.png"}
{"question": "Find $b$.", "answer": "18", "image_path": "train/442.png"}
{"question": "Find the area of the regular polygon. Round to the nearest tenth.", "answer": "584.2", "image_path": "train/443.png"}
{"question": "Find y.", "answer": "5 \\sqrt { 33 }", "image_path": "train/444.png"}
{"question": "Find x", "answer": "4", "image_path": "train/445.png"}
{"question": "$\\ln \\odot K$, $ M N=16$ and $m \\widehat{M N}=98$. Find the measure of $LN$. Round to the nearest hundredth.", "answer": "8.94", "image_path": "train/446.png"}
{"question": "Find the radius of $\\odot K$. Round to the nearest hundredth.", "answer": "19.00", "image_path": "train/447.png"}
{"question": "Find y.", "answer": "10 \\sqrt { 3 }", "image_path": "train/448.png"}
{"question": "Find the length of $CB$ in the isosceles triangle ABC. ", "answer": "7", "image_path": "train/449.png"}
{"question": "Find the area of the triangle. Round to the nearest hundredth.", "answer": "6.02", "image_path": "train/450.png"}
{"question": "Use parallelogram MNPR to find $z$", "answer": "6.1", "image_path": "train/451.png"}
{"question": "Find the length of $XW$", "answer": "9", "image_path": "train/452.png"}
{"question": "Use parallelogram ABCD to find $y$", "answer": "6", "image_path": "train/453.png"}
{"question": "In $\\odot R$, If $SU=16.2$, what is $RT$?", "answer": "8.1", "image_path": "train/454.png"}
{"question": "For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure. ", "answer": "\\frac { 3 } { 2 }", "image_path": "train/455.png"}
{"question": "In $\\odot O, \\overline{E C}$ and $\\overline{A B}$ are diameters, and $\\angle B O D \\cong \\angle D O E \\cong \\angle E O F \\cong \\angle F O A$\r\nFind $m\\widehat{C B F}$", "answer": "225", "image_path": "train/456.png"}
{"question": "In the figure, $ \\overline{GK} \\cong \\overline{GH}$ and $ \\overline{HK} \\cong \\overline{KJ}$. If $m \\angle HGK=42$, find $m \\angle HJK$.", "answer": "34.5", "image_path": "train/457.png"}
{"question": "WXYZ is a kite. If $m\\angle WXY = 13x + 24$, $m\\angle WZY = 35$, and $m\\angle ZWX = 13x + 14$, find $m\\angle ZYX$.", "answer": "105", "image_path": "train/458.png"}
{"question": "Find $y$ in the given parallelogram", "answer": "2", "image_path": "train/459.png"}
{"question": "Find z", "answer": "4 \\sqrt { 3 }", "image_path": "train/460.png"}
{"question": "Line $l$ is parallel to line $m$. What is the value of $x$?", "answer": "50", "image_path": "train/461.png"}
{"question": "If $AD=27,AB=8$, and $AE=12$, find $BC$.", "answer": "10", "image_path": "train/462.png"}
{"question": "Find y. Round to the nearest tenth.", "answer": "25.9", "image_path": "train/463.png"}
{"question": "Find $x$.", "answer": "45", "image_path": "train/464.png"}
{"question": "Find $m \\angle 2$.", "answer": "39", "image_path": "train/465.png"}
{"question": "Find x. Round to the nearest tenth, if necessary.", "answer": "14.3", "image_path": "train/466.png"}
{"question": "A plane travels from Des Moines to Phoenix, on to Atlanta, and back to Des Moines, as shown below. Find the distance in miles from Des Moines to Phoenix if the total trip was 3482 miles.", "answer": "1153", "image_path": "train/467.png"}
{"question": "Find VW", "answer": "12", "image_path": "train/468.png"}
{"question": "Find the area of the kite. ", "answer": "72", "image_path": "train/469.png"}
{"question": "Find $x$.", "answer": "18", "image_path": "train/470.png"}
{"question": "Find $y$ so that each quadrilateral is a parallelogram.", "answer": "9", "image_path": "train/471.png"}
{"question": "Find $m \\angle 1$.", "answer": "128", "image_path": "train/472.png"}
{"question": "Find x", "answer": "28.2", "image_path": "train/473.png"}
{"question": "Find $m \\angle 3$.", "answer": "55", "image_path": "train/474.png"}
{"question": "Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "10", "image_path": "train/475.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram", "answer": "9", "image_path": "train/476.png"}
{"question": "Find $m \\angle 2$.", "answer": "20", "image_path": "train/477.png"}
{"question": "Find y.", "answer": "4 \\sqrt { 3 }", "image_path": "train/478.png"}
{"question": "Find x", "answer": "8 \\sqrt { 3 }", "image_path": "train/479.png"}
{"question": "Polygons $FGHJK$ and $VWXUZ$ are similar regular pentagons. Find the scale factor.", "answer": "2:3", "image_path": "train/480.png"}
{"question": "Find x", "answer": "20", "image_path": "train/481.png"}
{"question": "In $\\odot Z, \\angle W Z X \\cong \\angle X Z Y, m \\angle V Z U=4 x$, $m \\angle U Z Y=2 x+24,$ and $\\overline{V Y}$ and $\\overline{W U}$ are diameters.\r\nFind $m\\widehat{W X}$", "answer": "52", "image_path": "train/482.png"}
{"question": "Polygon ABCD ~ polygon AEFG, $m\\angle AGF = 108$, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26.\r\nFind AG", "answer": "7.5", "image_path": "train/483.png"}
{"question": "Find the measure of $\\angle 5$ if $m∠4= m∠5$.", "answer": "32", "image_path": "train/484.png"}
{"question": "Circles $G, J,$ and $K$ all intersect at $L$ If $G H=10,$ find JK", "answer": "2.5", "image_path": "train/485.png"}
{"question": "Find x.", "answer": "\\sqrt { 285 }", "image_path": "train/486.png"}
{"question": "If PR || KL, KN = 9, LN = 16, PM = 2 KP, find ML", "answer": "20", "image_path": "train/487.png"}
{"question": "Find $HJ$.", "answer": "15", "image_path": "train/488.png"}
{"question": "Find the measure of $m \\widehat{GH}$.", "answer": "56", "image_path": "train/489.png"}
{"question": "If $\\overline{K H}$ is parallel to $\\overline{JI}$, find the measure of  $\\angle 3$", "answer": "90", "image_path": "train/490.png"}
{"question": "For trapezoid $R S T V, A$ and $B$ are midpoints of the legs. Find $V T$.", "answer": "4", "image_path": "train/491.png"}
{"question": "Find $m \\angle A$.", "answer": "20", "image_path": "train/492.png"}
{"question": "Use parallelogram ABCD to find $m \\angle FBC $", "answer": "34", "image_path": "train/493.png"}
{"question": "If $\\overline{W P}$ is a median and an angle bisector, $A P=3 y+11$, $P H=7 y-5$, $m \\angle H W P=x+12$, $m \\angle P A W=3 x-2$, and $m \\angle H W A=4 x-16$, find $y$.", "answer": "4", "image_path": "train/494.png"}
{"question": "In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\\angle 2$.", "answer": "80", "image_path": "train/495.png"}
{"question": "Find x", "answer": "\\sqrt { 15 }", "image_path": "train/496.png"}
{"question": "Find the perimeter or circumference of the figure. Round to the nearest tenth.", "answer": "8.6", "image_path": "train/497.png"}
{"question": "Find $x$ in the figure.", "answer": "34", "image_path": "train/498.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "50", "image_path": "train/499.png"}
{"question": "Find $x$.", "answer": "2", "image_path": "train/500.png"}
{"question": "Find AX if $E X=24$ and $D E=7$", "answer": "24", "image_path": "train/501.png"}
{"question": "One side of a square is a diameter of a circle. The length of one side of the square is 5 feet. To the nearest hundredth, what is the probability that a point chosen at random is in the shaded region?", "answer": "0.44", "image_path": "train/502.png"}
{"question": "Find x", "answer": "130", "image_path": "train/503.png"}
{"question": "Find the value of the variable $x$ in the figure.", "answer": "42", "image_path": "train/504.png"}
{"question": "Find $m\\angle U$", "answer": "60", "image_path": "train/505.png"}
{"question": "In the figure consisting of squares $A$, $B$, and $C$, $JK = 2KL$ and $KL = 2LM$. If the perimeter of the figure is 66 units, what is the area?", "answer": "189", "image_path": "train/506.png"}
{"question": "For trapezoid QRST, M and P are midpoints of the legs. If QR = 16, PM = 12, and TS = 4x, find x.", "answer": "2", "image_path": "train/507.png"}
{"question": "In the figure, $m∠3 = 43$. Find the measure of $\\angle 10$.", "answer": "137", "image_path": "train/508.png"}
{"question": "Find $RS$.", "answer": "20", "image_path": "train/509.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth if necessary.", "answer": "45.7", "image_path": "train/510.png"}
{"question": "In $\\odot Z, \\angle W Z X \\cong \\angle X Z Y, m \\angle V Z U=4 x$, $m \\angle U Z Y=2 x+24,$ and $\\overline{V Y}$ and $\\overline{W U}$ are diameters.\r\nFind $m\\widehat{U Y}$", "answer": "76", "image_path": "train/511.png"}
{"question": "Find $y$.", "answer": "16", "image_path": "train/512.png"}
{"question": "Polygon ABCD ~ polygon AEFG, $m\\angle AGF = 108$, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26.\r\nFind BC", "answer": "12.8", "image_path": "train/513.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "92", "image_path": "train/514.png"}
{"question": "Find the measure of the altitude drawn to the hypotenuse.", "answer": "7 \\sqrt { 3 }", "image_path": "train/515.png"}
{"question": "Find x. Round the angle measure to the nearest degree.", "answer": "72", "image_path": "train/516.png"}
{"question": "Quadrilateral DEFG is a rectangle. If DE = 14 + 2x and GF = 4(x - 3) + 6, find GF.", "answer": "34", "image_path": "train/517.png"}
{"question": "Find x.", "answer": "7 \\sqrt { 2 }", "image_path": "train/518.png"}
{"question": "Use parallelogram WXYZ to find $WZ$", "answer": "24", "image_path": "train/519.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "7", "image_path": "train/520.png"}
{"question": "In the figure, $m∠1 = 123$. Find the measure of $\\angle 6$.", "answer": "57", "image_path": "train/521.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "106.1", "image_path": "train/522.png"}
{"question": "Find $m \\widehat{TU}$.", "answer": "46", "image_path": "train/523.png"}
{"question": "Find $BC$.", "answer": "23", "image_path": "train/524.png"}
{"question": "Quadrilateral $WXYZ$ is a rectangle. Find the measure of $\\angle 8$ if $m∠1 = 30$.", "answer": "30", "image_path": "train/525.png"}
{"question": "Find $UZ$.", "answer": "18", "image_path": "train/526.png"}
{"question": "Find x", "answer": "3", "image_path": "train/527.png"}
{"question": "For isosceles trapezoid $X Y Z W$ find $m \\angle Z$", "answer": "110", "image_path": "train/528.png"}
{"question": "Find the area of the quadrilateral.", "answer": "499.5", "image_path": "train/529.png"}
{"question": "Assume that the segment is tangent, find the value of $x$.", "answer": "\\sqrt { 93 }", "image_path": "train/530.png"}
{"question": "Find $m\\angle E$", "answer": "102", "image_path": "train/531.png"}
{"question": "Find $x$ so that $ m \\parallel n $.", "answer": "9", "image_path": "train/532.png"}
{"question": "Use parallelogram ABCD to find BC", "answer": "9", "image_path": "train/533.png"}
{"question": "Find $y$.", "answer": "5", "image_path": "train/534.png"}
{"question": "Find $x$.", "answer": "115", "image_path": "train/535.png"}
{"question": "Find $WT$, if $ZX = 20$ and $TY = 15$", "answer": "5", "image_path": "train/536.png"}
{"question": "Each pair of polygons is similar. Find x", "answer": "30", "image_path": "train/537.png"}
{"question": "The segment is tangent to the circle. Find $x$. Round to the nearest tenth.", "answer": "10.7", "image_path": "train/538.png"}
{"question": "Find $m\\angle A$", "answer": "90", "image_path": "train/539.png"}
{"question": "Find the measure of $\\angle 6$ if $\\overline{A B} \\perp \\overline{B C}$.", "answer": "26", "image_path": "train/540.png"}
{"question": "Find $m \\angle 2$.", "answer": "73", "image_path": "train/541.png"}
{"question": "$\\odot P$ is inscribed in equilateral triangle $LMN$. What is the circumference of $\\odot P$?", "answer": "\\frac { 8 } { \\sqrt 3 } \\pi", "image_path": "train/542.png"}
{"question": "Find $E D$ if $A B=6, B C=4,$ and $A E=9$", "answer": "6", "image_path": "train/543.png"}
{"question": "In rhombus $A B C D, m \\angle D A B=2, m \\angle A D C$ and $C B=6$. Find DA", "answer": "6", "image_path": "train/544.png"}
{"question": "Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "answer": "5", "image_path": "train/545.png"}
{"question": "Use a Pythagorean Triple to find x.", "answer": "50", "image_path": "train/546.png"}
{"question": "Find the perimeter of the figure.", "answer": "44", "image_path": "train/547.png"}
{"question": "Find the measure of $\\angle 4$ in the figure.", "answer": "60", "image_path": "train/548.png"}
{"question": "In the figure, $\\overline{CP}$ is an altitude, $\\overline{CQ}$ is the angle bisector of $∠ACB$, and $R$ is the midpoint of $\\overline{AB}$. Find  $x$ if $m∠APC=72+x$.", "answer": "18", "image_path": "train/549.png"}
{"question": " In $\\odot Z, P Z=Z Q$, $X Y=4 a-5,$ and $S T=-5 a+13$\r\nFind $S Q$", "answer": "1.5", "image_path": "train/550.png"}
{"question": "If $\\overline{PR} \\| \\overline{WX}, WX=10, XY=6, WY=8, RY=5,$ and $PS=3,$ find $PQ$.", "answer": "6", "image_path": "train/551.png"}
{"question": "Find $RS$.", "answer": "25", "image_path": "train/552.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "500", "image_path": "train/553.png"}
{"question": "In $\\triangle ACE$, P is the centroid. $PF=6$ and $AD=15$. Find $PC$.", "answer": "12", "image_path": "train/554.png"}
{"question": "If $M D=7,$ find $R I$", "answer": "14", "image_path": "train/555.png"}
{"question": "Find $\\angle 6$", "answer": "110", "image_path": "train/556.png"}
{"question": "Quadrilateral DEFG is a rectangle. If $DF = 2(x + 5) - 7$ and $EG = 3(x - 2)$, find EG.", "answer": "21", "image_path": "train/557.png"}
{"question": "Find $m \\angle M$.", "answer": "30", "image_path": "train/558.png"}
{"question": "Refer to trapezoid $CDFG$ with median $\\overline{HE}$. Find $GF$.", "answer": "30", "image_path": "train/559.png"}
{"question": "Find $m \\angle H$.", "answer": "106", "image_path": "train/560.png"}
{"question": "Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "17.1", "image_path": "train/561.png"}
{"question": "Find the measure of $\\angle S$", "answer": "71", "image_path": "train/562.png"}
{"question": "Find $y$ so that each quadrilateral is a parallelogram.", "answer": "24", "image_path": "train/563.png"}
{"question": "Find x.", "answer": "12", "image_path": "train/564.png"}
{"question": "In $\\odot G, m \\angle A G B=30$ and $\\overline{C G} \\perp \\overline{G D}$.\r\nFind $m \\widehat{B C}$", "answer": "60", "image_path": "train/565.png"}
{"question": "In the figure, $m ∠ 12 = 64$. Find the measure of $ \\angle 11$.", "answer": "116", "image_path": "train/566.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "480", "image_path": "train/567.png"}
{"question": "Use parallelogram to find $b$", "answer": "3", "image_path": "train/568.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth, if necessary.", "answer": "10.0", "image_path": "train/569.png"}
{"question": "Find $BD$.", "answer": "5", "image_path": "train/570.png"}
{"question": "If $QR=2$, $XW=12$, $QW=15$, and $ST=5$, find $WV$.", "answer": "7.5", "image_path": "train/571.png"}
{"question": "Express the ratio of $\\tan C$ as a decimal to the nearest hundredth.", "answer": "0.75", "image_path": "train/572.png"}
{"question": "Find x.", "answer": "6", "image_path": "train/573.png"}
{"question": "In rhombus LMPQ, $m \\angle Q L M=2 x^{2}-10$, $m \\angle Q P M=8 x$,  and $M P=10$ . \r\nFind $m\\angle LQM$", "answer": "70", "image_path": "train/574.png"}
{"question": "Find $y$.", "answer": "7.5", "image_path": "train/575.png"}
{"question": "For trapezoid QRTU, V and S are midpoints of the legs. If QR = 12 and UT = 22, find VS.", "answer": "17", "image_path": "train/576.png"}
{"question": "Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "3.1", "image_path": "train/577.png"}
{"question": "$J$ is the incenter of $\\angle ABC$. Find $JF$.", "answer": "9", "image_path": "train/578.png"}
{"question": "Find the area of the trapezoid.", "answer": "84", "image_path": "train/579.png"}
{"question": "Find z.", "answer": "\\sqrt { 646 }", "image_path": "train/580.png"}
{"question": "Find x", "answer": "\\frac { 40 } { 3 }", "image_path": "train/581.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "286", "image_path": "train/582.png"}
{"question": "What is the perimeter of the triangle shown below? Round to the nearest tenth.", "answer": "325.6", "image_path": "train/583.png"}
{"question": "Find $x$.", "answer": "60", "image_path": "train/584.png"}
{"question": "The diameters of $\\odot A, \\odot B,$ and $\\odot C$ are 10, 30 and 10 units, respectively. Find AZ if $\\overline{A Z} \\cong \\overline{C W}$ and $C W=2$\r\n", "answer": "2", "image_path": "train/585.png"}
{"question": "Find $m\\angle D$", "answer": "101", "image_path": "train/586.png"}
{"question": "Find the perimeter of the figure.", "answer": "50", "image_path": "train/587.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "1520", "image_path": "train/588.png"}
{"question": "The radius of $\\odot P$ is 5 and $P R=3$. Find QS", "answer": "8", "image_path": "train/589.png"}
{"question": "Find the area of the kite.", "answer": "10.5", "image_path": "train/590.png"}
{"question": "Quadrilateral WXYZ is a rectangle.  If $ZY = 2x + 3$ and $WX = x + 4$, find $WX$.", "answer": "5", "image_path": "train/591.png"}
{"question": "Find x. Round the side measure to the nearest tenth.", "answer": "37.2", "image_path": "train/592.png"}
{"question": "Find $YZ$.", "answer": "8", "image_path": "train/593.png"}
{"question": "In the figure, $m ∠1 = 58 $, $m ∠2 = 47 $, and $m ∠3 = 26 $. Find the measure of $∠8$.", "answer": "73", "image_path": "train/594.png"}
{"question": "For the pair of similar figures, find the area of the green figure.", "answer": "78.4", "image_path": "train/595.png"}
{"question": "Find the variable of $q$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "9.0", "image_path": "train/596.png"}
{"question": "Find the perimeter of $\\triangle A B C$", "answer": "30", "image_path": "train/597.png"}
{"question": "If $x=7 \\sqrt{3},$ find $CE$", "answer": "21", "image_path": "train/598.png"}
{"question": "Find x. Assume that any segment that appears to be tangent is tangent.", "answer": "5", "image_path": "train/599.png"}
{"question": "Find the measure of $\\angle 2$.", "answer": "53", "image_path": "train/600.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "57.9", "image_path": "train/601.png"}
{"question": "Find y", "answer": "16", "image_path": "train/602.png"}
{"question": "Find $y$ in the figure.", "answer": "15", "image_path": "train/603.png"}
{"question": "Find the exact circumference of the circle below.", "answer": "32 \\pi", "image_path": "train/604.png"}
{"question": "Find $x$.", "answer": "48", "image_path": "train/605.png"}
{"question": "Find the area of the composite figure. Round to the nearest tenth.", "answer": "357.0", "image_path": "train/606.png"}
{"question": "Find x.", "answer": "9 \\sqrt { 2 }", "image_path": "train/607.png"}
{"question": "Find z.", "answer": "6", "image_path": "train/608.png"}
{"question": "Find the area of the figure. Round to the nearest tenth.", "answer": "231", "image_path": "train/609.png"}
{"question": "Find $m \\angle X$", "answer": "108", "image_path": "train/610.png"}
{"question": "Find y.", "answer": "15", "image_path": "train/611.png"}
{"question": "Find x. Round to the nearest tenth.", "answer": "10.8", "image_path": "train/612.png"}
{"question": "Find the value of x.", "answer": "4.08", "image_path": "train/613.png"}
{"question": "Use the figure to find the indicated variable. Find $y$ if $m \\angle 3 = 4y + 30$ and $m \\angle 7 = 7y + 6$.", "answer": "8", "image_path": "train/614.png"}
{"question": "In $\\triangle CDF$, $K$ is the centroid and $DK=16$. Find $FG$.", "answer": "18", "image_path": "train/615.png"}
{"question": "Find the area of the shaded figure in square inches. Round to the nearest tenth.", "answer": "420", "image_path": "train/616.png"}
{"question": "Find the area of the figure.", "answer": "54.9", "image_path": "train/617.png"}
{"question": "Find the value of $f$ in the parallelogram", "answer": "14", "image_path": "train/618.png"}
{"question": "$J$ is the incenter of $\\angle ABC$. Find $m \\angle JAC$.", "answer": "24", "image_path": "train/619.png"}
{"question": "Find $m \\angle R C L$", "answer": "137", "image_path": "train/620.png"}
{"question": "Find x", "answer": "3 \\sqrt { 2 }", "image_path": "train/621.png"}
{"question": "Find x.", "answer": "32", "image_path": "train/622.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth.", "answer": "471.2", "image_path": "train/623.png"}
{"question": "If quadrilateral ABCD is a kite, what is $m \\angle C$?", "answer": "76", "image_path": "train/624.png"}
{"question": "Find the value of the variable $y$ in the figure.", "answer": "125", "image_path": "train/625.png"}
{"question": "In the figure, $m ∠1 = 53$. Find the measure of $∠4$.", "answer": "127", "image_path": "train/626.png"}
{"question": "Find $m \\angle S$.", "answer": "54", "image_path": "train/627.png"}
{"question": "Find x.", "answer": "\\frac { 15 } { 14 } \\sqrt { 19 }", "image_path": "train/628.png"}
{"question": "Find $x$ so that $p \\parallel q$.", "answer": "45", "image_path": "train/629.png"}
{"question": "If $MNPQ \\sim XYZW,$ find the scale factor of $MNPQ$ to $XYZW$.", "answer": "2", "image_path": "train/630.png"}
{"question": "Find $SP$.", "answer": "17", "image_path": "train/631.png"}
{"question": "$m∠9 = 2x - 4$, $m∠10 = 2x + 4$. Find the measure of $∠9$.", "answer": "86", "image_path": "train/632.png"}
{"question": "Find the measure of $m∠K$.", "answer": "53", "image_path": "train/633.png"}
{"question": "If $J,P,$ and $L$ are the midpoints of $\\overline{KH}, \\overline{HM}$ and $\\overline{MK}$, respectively. Find $y$.", "answer": "6", "image_path": "train/634.png"}
{"question": "If $J,P,$ and $L$ are the midpoints of $\\overline{KH}, \\overline{HM}$ and $\\overline{MK}$, respectively. Find $z$.", "answer": "1", "image_path": "train/635.png"}
{"question": "If QRST is a parallelogram, what is the value of x?", "answer": "13", "image_path": "train/636.png"}
{"question": "In $\\odot F$, $\\overline{AB} \\cong \\overline{BC}$, $DF=3x-7$, and $FE=x+9$. What is $x$?", "answer": "8", "image_path": "train/637.png"}
{"question": "Find $x$. A = 153 in$^2$.", "answer": "17", "image_path": "train/638.png"}
{"question": "What is the area of the sector?", "answer": "\\frac { \\pi } { 4 }", "image_path": "train/639.png"}
{"question": "Find $m\\angle J$", "answer": "150", "image_path": "train/640.png"}
{"question": "Find x", "answer": "3", "image_path": "train/641.png"}
{"question": "Each pair of polygons is similar. Find y", "answer": "70", "image_path": "train/642.png"}
{"question": "$a=8, b=15,$ and $c=17$ find $tanB$", "answer": "1.88", "image_path": "train/643.png"}
{"question": "Find $z$ in the figure.", "answer": "142", "image_path": "train/644.png"}
{"question": "Find the measure of $\\angle 1 $ if $\\overline{A B} \\perp \\overline{B C}$.", "answer": "76", "image_path": "train/645.png"}
{"question": "Find AC", "answer": "7 \\sqrt { 3 }", "image_path": "train/646.png"}
{"question": "Find $m \\angle K$.", "answer": "97", "image_path": "train/647.png"}
{"question": "In $\\triangle JKL$, $PT=2$. Find $KP$.", "answer": "4", "image_path": "train/648.png"}
{"question": "Find $m\\angle Z$", "answer": "144", "image_path": "train/649.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "115", "image_path": "train/650.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "1200", "image_path": "train/651.png"}
{"question": "Find $m\\angle K$", "answer": "62", "image_path": "train/652.png"}
{"question": "Find $m \\widehat {AC}$.", "answer": "48", "image_path": "train/653.png"}
{"question": "Find $x$.", "answer": "10", "image_path": "train/654.png"}
{"question": "Find the value of $x$ in each diagram", "answer": "44", "image_path": "train/655.png"}
{"question": "Find x", "answer": "4", "image_path": "train/656.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "60", "image_path": "train/657.png"}
{"question": "$ \\triangle RST$ is a right triangle. Find $m∠R$.", "answer": "60", "image_path": "train/658.png"}
{"question": "Lines $l$, $m$, and $n$ are perpendicular bisectors of $\\triangle PQR$ and meet at $T$. If $TQ = 2x$, $PT = 3y - 1$, and $TR = 8$, find $x$.", "answer": "4", "image_path": "train/659.png"}
{"question": "Find x", "answer": "7 \\sqrt { 3 }", "image_path": "train/660.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "99", "image_path": "train/661.png"}
{"question": "Find $x$ if $\\overline{MS}$ is an altitude of $\\triangle MNQ$, $m\\angle 1 = 3x + 11$, and $m \\angle 2 = 7x + 9$.", "answer": "7", "image_path": "train/662.png"}
{"question": "Find $z$ in the figure.", "answer": "42", "image_path": "train/663.png"}
{"question": "$\\triangle PQS \\cong \\triangle RQS$. Find $y$.", "answer": "8", "image_path": "train/664.png"}
{"question": "$P$ is the incenter of $\\angle XYZ$. Find $m \\angle LZP$.", "answer": "32", "image_path": "train/665.png"}
{"question": "The pair of polygons is similar. Find AB", "answer": "4", "image_path": "train/666.png"}
{"question": "isosceles trapezoid TWYZ with $\\angle Z \\cong \\angle Y, m \\angle Z=30 x$, $\\angle T \\cong \\angle W,$ and $m \\angle T=20 x$, find $\\angle T$", "answer": "72", "image_path": "train/667.png"}
{"question": "Find y.", "answer": "6 \\sqrt { 2 }", "image_path": "train/668.png"}
{"question": "Find y.", "answer": "\\frac { 2 } { 3 } \\sqrt { 5 }", "image_path": "train/669.png"}
{"question": "$\\overline{E C}$ and $\\overline{A B}$ are diameters of $\\odot O$.  Find its measure of $\\widehat{ACE}$.", "answer": "270", "image_path": "train/670.png"}
{"question": "In $\\odot O, \\overline{E C}$ and $\\overline{A B}$ are diameters, and $\\angle B O D \\cong \\angle D O E \\cong \\angle E O F \\cong \\angle F O A$\r\nFind $m\\widehat{A C B}$", "answer": "180", "image_path": "train/671.png"}
{"question": "Find BD", "answer": "1.8", "image_path": "train/672.png"}
{"question": "If $m \\widehat{F E}=118, m \\widehat{A B}=108$, $m \\angle E G B=52,$ and $m \\angle E F B=30$\r\nFind $m \\widehat{A C}$", "answer": "30", "image_path": "train/673.png"}
{"question": " The diagonals of rectangle $A B C D$ each have a length of 56 feet. If $m \\angle B A C=42^{\\circ}$, what is the length of $\\overline{A B}$ to the nearest tenth of a foot?", "answer": "41.6", "image_path": "train/674.png"}
{"question": "In $\\triangle PQR$, $\\overline{ST} \\| \\overline{R Q}$ . If  $PT=7.5$, $TQ=3$, and $SR=2.5$, find $PS$.", "answer": "6.25", "image_path": "train/675.png"}
{"question": "Find x", "answer": "7", "image_path": "train/676.png"}
{"question": "Find the area of the regular polygon. Round to the nearest tenth.", "answer": "212.1", "image_path": "train/677.png"}
{"question": "The area of $▱ A B C D$ is 150 square meters. The area of $▱ F G H J$ is 54 square meters. If $▱ A B C D \\sim ▱ F G H J$, find the scale factor of $▱ F G H J$ to $▱ A B C D$.", "answer": "\\frac { 3 } { 5 }", "image_path": "train/678.png"}
{"question": "Quadrilateral ABCD is a rectangle. Find y", "answer": "5", "image_path": "train/679.png"}
{"question": "In the figure, $a ∥ b, c ∥ d$, and $m∠4 = 57$. Find the measure of $\\angle 8$.", "answer": "57", "image_path": "train/680.png"}
{"question": "Use parallelogram to find $y$", "answer": "5", "image_path": "train/681.png"}
{"question": "If $\\frac{I J}{X J}=\\frac{HJ}{YJ}, m \\angle W X J=130$\r\nand $m \\angle WZG=20,$ find $m \\angle JHI$", "answer": "70", "image_path": "train/682.png"}
{"question": "Find x", "answer": "30", "image_path": "train/683.png"}
{"question": "Find x. Round to the nearest tenth, if necessary.", "answer": "15", "image_path": "train/684.png"}
{"question": "$UJ=9, VJ=3$, and $ZT=18$. Find $ZJ$.", "answer": "12", "image_path": "train/685.png"}
{"question": "Find the area of the triangle. Round to the nearest tenth if necessary.", "answer": "6", "image_path": "train/686.png"}
{"question": "For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure. ", "answer": "\\frac { 6 } { 5 }", "image_path": "train/687.png"}
{"question": "Find x.", "answer": "3", "image_path": "train/688.png"}
{"question": "$JKMN$ is a rectangle. If $NQ=2x+3$ and $QK=5x-9$, find $JQ$.", "answer": "11", "image_path": "train/689.png"}
{"question": "Find the perimeter of the $\\triangle A B C,$ if $\\triangle A B C \\sim \\triangle C B D, A D=5$, $C D=12,$ and $B C=31.2$", "answer": "78", "image_path": "train/690.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "4185", "image_path": "train/691.png"}
{"question": "Find $m \\angle 2$.", "answer": "59", "image_path": "train/692.png"}
{"question": "ABCD is a rhombus. If EB = 9, AB = 12 and $m\\angle ABD = 55$ . Find $m\\angle BDA$", "answer": "55", "image_path": "train/693.png"}
{"question": "Find y in the figure.", "answer": "40", "image_path": "train/694.png"}
{"question": "If WXYZ is a kite, find $m\\angle Z$", "answer": "75", "image_path": "train/695.png"}
{"question": "Find $x$.", "answer": "7", "image_path": "train/696.png"}
{"question": "Find $m\\angle T$", "answer": "46", "image_path": "train/697.png"}
{"question": "Each pair of polygons is similar. Find x", "answer": "27", "image_path": "train/698.png"}
{"question": "Find $SR$.", "answer": "24", "image_path": "train/699.png"}
{"question": "Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "answer": "10", "image_path": "train/700.png"}
{"question": "Find $AC$ if $AC=x-3$, $BE=20, AB=16,$ and $CD=x+5$", "answer": "32", "image_path": "train/701.png"}
{"question": "In the figure, $QR \\| TS$, $QT \\| RS$, and $m \\angle 1=131$. Find the measure of $\\angle 6$. ", "answer": "131", "image_path": "train/702.png"}
{"question": "In $\\odot P, m \\widehat{E N}=66$ and $m \\angle G P M=89$ . \r\nFind $m \\angle G N M$", "answer": "44.5", "image_path": "train/703.png"}
{"question": "Find $FH$.", "answer": "12", "image_path": "train/704.png"}
{"question": "If $m\\angle ZXW = x - 11$ and $m \\angle WZX = x - 9$, find $m\\angle ZXY$.", "answer": "46", "image_path": "train/705.png"}
{"question": "Find $m\\angle F$", "answer": "122", "image_path": "train/706.png"}
{"question": "Express the ratio of $\\cos L$ as a decimal to the nearest hundredth.", "answer": "0.92", "image_path": "train/707.png"}
{"question": "What is the length of $\\overline{EF}$?", "answer": "26", "image_path": "train/708.png"}
{"question": "Find $m \\widehat {TS}$.", "answer": "144", "image_path": "train/709.png"}
{"question": "Find the area of the sector. Round to the nearest tenth.", "answer": "2.5", "image_path": "train/710.png"}
{"question": "In quadrilateral $P Q R S, P Q=721, Q R=547$, $R S=593, P S=756,$ and $m \\angle P=58 .$ \r\nFind $m\\angle R$", "answer": "77.8", "image_path": "train/711.png"}
{"question": "Find $m \\angle B$.", "answer": "36", "image_path": "train/712.png"}
{"question": "Find the perimeter of $\\triangle D E F$ if $\\triangle D E F \\sim \\triangle A B C$", "answer": "24", "image_path": "train/713.png"}
{"question": "Find $x$ so that $ m \\parallel n $.", "answer": "15", "image_path": "train/714.png"}
{"question": "Find the area of the quadrilateral.", "answer": "104", "image_path": "train/715.png"}
{"question": "In $\\triangle EDF$, $T$ is the centroid and $FT=12$. Find $TQ$.", "answer": "6", "image_path": "train/716.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "8", "image_path": "train/717.png"}
{"question": "If $\\triangle J K L \\sim \\triangle P Q R$ and the area of $\\triangle J K L$ is\r\n30 square inches, find the area of $\\triangle P Q R$。", "answer": "46.9", "image_path": "train/718.png"}
{"question": "Find $RT$.", "answer": "15", "image_path": "train/719.png"}
{"question": "Find the measure of $\\angle 3$.", "answer": "42", "image_path": "train/720.png"}
{"question": "$\\overline{JH}$ is tangent to $\\odot G$ at $J$. Find the value of $x$.", "answer": "5", "image_path": "train/721.png"}
{"question": "Find $x$. $A = 177$ cm$^2$.", "answer": "16.2", "image_path": "train/722.png"}
{"question": "In the figure, $QR \\| TS$, $QT \\| RS$, and $m \\angle 1=131$. Find the measure of $\\angle 5$. ", "answer": "49", "image_path": "train/723.png"}
{"question": "Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "answer": "4", "image_path": "train/724.png"}
{"question": "In $\\odot A$, $WX=XY=22$. Find $AB$.", "answer": "10", "image_path": "train/725.png"}
{"question": "Find y", "answer": "5 \\sqrt { 2 }", "image_path": "train/726.png"}
{"question": "Find the area of the blue region.", "answer": "114.2", "image_path": "train/727.png"}
{"question": "Find x. Round the side measure to the nearest tenth.", "answer": "50.6", "image_path": "train/728.png"}
{"question": "Find the measure of $∠T$ to the nearest tenth.", "answer": "33.7", "image_path": "train/729.png"}
{"question": "In $\\odot J$, $GH=9$ and $KL=4x+1$. Find $x$.", "answer": "2", "image_path": "train/730.png"}
{"question": "Find $x$ so that $m || n$.", "answer": "36", "image_path": "train/731.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "55.6", "image_path": "train/732.png"}
{"question": "Find x. Round to the nearest hundredth.", "answer": "7.21", "image_path": "train/733.png"}
{"question": "Find $x$ so that each quadrilateral is a parallelogram.", "answer": "12", "image_path": "train/734.png"}
{"question": "Find x", "answer": "\\frac { 50 } { 3 }", "image_path": "train/735.png"}
{"question": "The diameters of $\\odot A, \\odot B,$ and $\\odot C$ are 10, 30 and 10 units, respectively. Find BY if $\\overline{A Z} \\cong \\overline{C W}$ and $C W=2$.", "answer": "12", "image_path": "train/736.png"}
{"question": "Find $m \\angle 4$.", "answer": "55", "image_path": "train/737.png"}
{"question": "Find $x$ if $\\odot M \\cong \\odot N$.", "answer": "9", "image_path": "train/738.png"}
{"question": "Find $x$ in the figure.", "answer": "112", "image_path": "train/739.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "39.0", "image_path": "train/740.png"}
{"question": "Find AC", "answer": "9.6", "image_path": "train/741.png"}
{"question": "What is the total area of the figure?", "answer": "368", "image_path": "train/742.png"}
{"question": "Find the exact circumference of the circle.", "answer": "9 \\pi", "image_path": "train/743.png"}
{"question": "$m$ is the perpendicular bisector of $XZ$, $WZ=4a-15$ and $WZ=a+12$. Find $WX$.", "answer": "21", "image_path": "train/744.png"}
{"question": "Find the area of the triangle. Round to the nearest tenth if necessary.", "answer": "96", "image_path": "train/745.png"}
{"question": "Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.", "answer": "114.2", "image_path": "train/746.png"}
{"question": "In $\\odot A, m \\angle E A D=42$. Find $m \\widehat{B C}$", "answer": "42", "image_path": "train/747.png"}
{"question": "$\\triangle RST \\cong \\triangle VUT$. Find $x$.", "answer": "2", "image_path": "train/748.png"}
{"question": "In $\\odot R, S U=20, Y W=20,$ and $m \\widehat{Y X}=45$.\r\nFind $m\\widehat{Y W}$", "answer": "90", "image_path": "train/749.png"}
{"question": "Find the area of the trapezoid.", "answer": "96", "image_path": "train/750.png"}
{"question": "Find y in the parallelogram", "answer": "6", "image_path": "train/751.png"}
{"question": "Find $x$.", "answer": "4", "image_path": "train/752.png"}
{"question": "Find $AF$.", "answer": "10.8", "image_path": "train/753.png"}
{"question": "Find y.", "answer": "10", "image_path": "train/754.png"}
{"question": "Two triangles are similar. Find $x$.", "answer": "16.5", "image_path": "train/755.png"}
{"question": "Find $x$ so that $ m \\parallel n $.", "answer": "16", "image_path": "train/756.png"}
{"question": "Given right triangle $XYZ$ with hypotenuse $\\overline{XY}$, $YP$ is equal to $YZ$. If $m ∠PYZ = 26$, find $m ∠XZP$.", "answer": "13", "image_path": "train/757.png"}
{"question": "The segment is tangent to the circle. Find $x$.", "answer": "5 \\sqrt { 10 }", "image_path": "train/758.png"}
{"question": "Find $m \\angle P$.", "answer": "35", "image_path": "train/759.png"}
{"question": "For the pair of similar figures, use the given areas to find $x$.", "answer": "6.0", "image_path": "train/760.png"}
{"question": "Find y.", "answer": "\\frac { 12 } { 5 } \\sqrt { 11 }", "image_path": "train/761.png"}
{"question": "Find x.", "answer": "\\frac { 15 \\sqrt { 2 } } { 2 }", "image_path": "train/762.png"}
{"question": "Find $CD$.", "answer": "4", "image_path": "train/763.png"}
{"question": "Triangle $A D C$ is circumscribed about $\\odot O .$ Find the perimeter of $\\triangle A D C$ if $E C=D E+A F$", "answer": "100", "image_path": "train/764.png"}
{"question": "Find $m \\angle 5$.", "answer": "57", "image_path": "train/765.png"}
{"question": "Rhombus $WXYZ$ has an area of 100 square meters. Find $WY$ if $XZ = 10$ meters.", "answer": "20", "image_path": "train/766.png"}
{"question": "Find $x$.", "answer": "10", "image_path": "train/767.png"}
{"question": "Find x.", "answer": "13 \\sqrt { 2 }", "image_path": "train/768.png"}
{"question": "Find $x$.", "answer": "81.5", "image_path": "train/769.png"}
{"question": "Find $x$ so that the quadrilateral is a parallelogram.", "answer": "30", "image_path": "train/770.png"}
{"question": "Find y", "answer": "21", "image_path": "train/771.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "239", "image_path": "train/772.png"}
{"question": "Find the area of quadrilateral $XYZW$ if $XZ = 39$, $HW = 20$, and $YG = 21$.", "answer": "799.5", "image_path": "train/773.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "4", "image_path": "train/774.png"}
{"question": "In rhombus $A B C D, A B=2 x+3$ and $B C=5 x$. Find x.", "answer": "1", "image_path": "train/775.png"}
{"question": "Find y.", "answer": "6 \\sqrt { 3 }", "image_path": "train/776.png"}
{"question": "Find the area of the kite.", "answer": "72", "image_path": "train/777.png"}
{"question": "Find the value  of $x$ in each diagram", "answer": "93", "image_path": "train/778.png"}
{"question": "Find the measure of $\\angle T$.", "answer": "77", "image_path": "train/779.png"}
{"question": "In the triangle, what is the measure of $∠Z$?", "answer": "18", "image_path": "train/780.png"}
{"question": "Quadrilateral ABCD is a rhombus. If $m\\angle ABC = 2x – 7$ and $m\\angle BCD = 2x + 3$, find $m\\angle DAB$.", "answer": "95", "image_path": "train/781.png"}
{"question": "The two polygons are similar. Find x.", "answer": "13.5", "image_path": "train/782.png"}
{"question": "In $\\triangle CDF$, $K$ is the centroid and $DK=16$. Find $KH$.", "answer": "8", "image_path": "train/783.png"}
{"question": "Find $z$ in the figure.", "answer": "73", "image_path": "train/784.png"}
{"question": "$\\overline{PQ}$ is tangent to the circle. Find $x$. Round to the nearest tenth.", "answer": "5.2", "image_path": "train/785.png"}
{"question": "Find the ratio of $MS$ to $SP$, given that $MNPQ$ is a parallelogram with $MR=\\frac{1}{4} MN$", "answer": "0.5", "image_path": "train/786.png"}
{"question": "Find x so that $GJ \\parallel FK$. $H J=x-5, J K=15, F G=18, H G=x-4\r\n", "answer": "10", "image_path": "train/787.png"}
{"question": "In $\\triangle P Q R, R S=3$ and $Q S=14 .$ Find $P S$", "answer": "\\sqrt { 42 }", "image_path": "train/788.png"}
{"question": "JKLM is a rhombus. If $CK = 8$ and $JK = 10$, Find $JC$.", "answer": "6", "image_path": "train/789.png"}
{"question": "Find x", "answer": "60", "image_path": "train/790.png"}
{"question": "Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "13", "image_path": "train/791.png"}
{"question": "Find y", "answer": "\\sqrt { 33 }", "image_path": "train/792.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth.", "answer": "39.3", "image_path": "train/793.png"}
{"question": "For the pair of similar figures, use the given areas to find $x$.", "answer": "5", "image_path": "train/794.png"}
{"question": "Find x. Round the side measure to the nearest tenth.", "answer": "107.9", "image_path": "train/795.png"}
{"question": "Equilateral pentagon $P Q R S T$ is inscribed in $\\odot U$.\r\nFind $m \\angle P Q R$", "answer": "108", "image_path": "train/796.png"}
{"question": "If $LK=4,MP=3,PQ=6,KJ=2,RS=6$, and $LP=2$, find $QR$.", "answer": "3", "image_path": "train/797.png"}
{"question": "Circle $J$ has a radius of $10$ units, $\\odot K$ has a radius of $8$ units, and $BC=5.4$ units. Find $AB$.", "answer": "14.6", "image_path": "train/798.png"}
{"question": "Find the measure of $∠R$ to the nearest tenth.", "answer": "70.9", "image_path": "train/799.png"}
{"question": "Find y", "answer": "4 \\sqrt { 3 }", "image_path": "train/800.png"}
{"question": "Find $x$.", "answer": "66", "image_path": "train/801.png"}
{"question": "Find x.", "answer": "17", "image_path": "train/802.png"}
{"question": "Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.", "answer": "30.4", "image_path": "train/803.png"}
{"question": "In the figure, $ \\triangle ABC$ is isosceles, $ \\triangle DCE$ is equilateral, and $ \\triangle FCG$ is isosceles. Find the measures of the $\\angle 4$ at vertex $C$.", "answer": "17", "image_path": "train/804.png"}
{"question": "Find y. Round to the nearest tenth, if necessary.", "answer": "22.5", "image_path": "train/805.png"}
{"question": "Find y", "answer": "4 \\sqrt { 3 }", "image_path": "train/806.png"}
{"question": "Find $XZ$ of isosceles $\\triangle XYZ$", "answer": "12", "image_path": "train/807.png"}
{"question": "Find $m \\angle 2$.", "answer": "24", "image_path": "train/808.png"}
{"question": "Find x.", "answer": "0.5", "image_path": "train/809.png"}
{"question": "If $J,P,$ and $L$ are the midpoints of $\\overline{KH}, \\overline{HM}$ and $\\overline{MK}$, respectively. Find $x$.", "answer": "4.75", "image_path": "train/810.png"}
{"question": "If $ABCDE \\sim PQRST,$ find the scale factor of $ABCDE$ to $PQRST$.", "answer": "\\frac { 4 } { 3 }", "image_path": "train/811.png"}
{"question": "Quadrilateral DEFG is a rectangle. If $FD = 3x - 7$ and $EG = x + 5$, find $EG$.", "answer": "6", "image_path": "train/812.png"}
{"question": "Find the value of $x$ in the figure below.", "answer": "128", "image_path": "train/813.png"}
{"question": "If KLMN is a parallelogram, find the value of the\r\nindicated variable. Find y", "answer": "11", "image_path": "train/814.png"}
{"question": "What is the length of $R T ?$", "answer": "5 \\sqrt { 2 }", "image_path": "train/815.png"}
{"question": "Find $\\angle 8$", "answer": "90", "image_path": "train/816.png"}
{"question": "What is the perimeter of the figure?", "answer": "20", "image_path": "train/817.png"}
{"question": "Find $x$.", "answer": "70", "image_path": "train/818.png"}
{"question": "Find the measure of $\\angle A$. Round to the nearest degree.", "answer": "74", "image_path": "train/819.png"}
{"question": "Find $m\\angle B$", "answer": "112", "image_path": "train/820.png"}
{"question": "Find y. Round to the nearest tenth.", "answer": "11.7", "image_path": "train/821.png"}
{"question": "Use a calculator to find the measure of $∠J$ to the nearest degree.", "answer": "45", "image_path": "train/822.png"}
{"question": "Express the ratio of $\\sin A$ as a decimal to the nearest hundredth.", "answer": "0.80", "image_path": "train/823.png"}
{"question": "WXYZ is a square. If $WT = 3$, find $m \\angle WTZ$", "answer": "90", "image_path": "train/824.png"}
{"question": "Find x", "answer": "18", "image_path": "train/825.png"}
{"question": "In the figure, $m ∠9 = 75$. Find the measure of $\\angle 12$.", "answer": "105", "image_path": "train/826.png"}
{"question": "Find $m \\widehat{Y C}$.", "answer": "60", "image_path": "train/827.png"}
{"question": "Find the perimeter of the figure. Round to the nearest hundredth, if necessary.", "answer": "9.2", "image_path": "train/828.png"}
{"question": "In $\\odot R, S U=20, Y W=20,$ and $m \\widehat{Y X}=45$.\r\nFind WZ", "answer": "10", "image_path": "train/829.png"}
{"question": "$a=14, b=48,$ and $c=50$ find $tanA$", "answer": "0.29", "image_path": "train/830.png"}
{"question": "Find $R S$ if $P Q=12, Q R=2,$ and $T S=3$", "answer": "4", "image_path": "train/831.png"}
{"question": "Use parallelogram JKLM to find m \\angle JKL if $J K=2 b+3$ and $J M=3 a$.", "answer": "80", "image_path": "train/832.png"}
{"question": "Find $m \\angle 7$.", "answer": "70", "image_path": "train/833.png"}
{"question": "Find $RS$.", "answer": "8", "image_path": "train/834.png"}
{"question": "Find the area of the figure to the nearest tenth.", "answer": "87.5", "image_path": "train/835.png"}
{"question": "Find x. Round side measures to the nearest tenth.", "answer": "7.7", "image_path": "train/836.png"}
{"question": "Find x.", "answer": "85", "image_path": "train/837.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "63.2", "image_path": "train/838.png"}
{"question": "Find x", "answer": "60", "image_path": "train/839.png"}
{"question": "Which of the following statements about the figure is true?", "answer": "a + b = 90", "image_path": "train/840.png"}
{"question": "$\\overline{JH}, \\overline{JP},$ and $\\overline{PH}$ are midsegments of $\\triangle KLM$. Find $x$.", "answer": "57", "image_path": "train/841.png"}
{"question": "$Q$ is the incenter of $\\triangle JKL$. Find $m \\angle QJK$.", "answer": "35", "image_path": "train/842.png"}
{"question": "In $\\odot S, m \\angle T S R=42$\r\nFind $m\\widehat{KT}$", "answer": "138", "image_path": "train/843.png"}
{"question": "Find the measure of $\\angle 2$.", "answer": "25", "image_path": "train/844.png"}
{"question": "Find $y$ in the figure.", "answer": "15", "image_path": "train/845.png"}
{"question": "Quadrilateral ABCD is a rhombus. If $m\\angle BCD$ = 64, find $m\\angle BAC$.", "answer": "32", "image_path": "train/846.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth.", "answer": "1.5", "image_path": "train/847.png"}
{"question": "Find $GH$", "answer": "39", "image_path": "train/848.png"}
{"question": "Find $x$.", "answer": "3", "image_path": "train/849.png"}
{"question": "In the figure, $ \\overline{JM} \\cong \\overline{PM}$ and $ \\overline{ML} \\cong \\overline{PL}$. If $m \\angle PLJ=58$, find $m \\angle PJL$.", "answer": "30.5", "image_path": "train/850.png"}
{"question": "Find $m\\angle 3$", "answer": "32", "image_path": "train/851.png"}
{"question": "What is the value of $x$ if $m \\widehat{NR}=62$ and $m \\widehat {NP}=108$?", "answer": "64", "image_path": "train/852.png"}
{"question": "Find y.", "answer": "4 \\sqrt { 6 }", "image_path": "train/853.png"}
{"question": "Find $m\\angle E$", "answer": "158", "image_path": "train/854.png"}
{"question": "For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.", "answer": "\\frac { 1 } { \\sqrt { 3 } }", "image_path": "train/855.png"}
{"question": "Find x. Round the side measure to the nearest tenth.", "answer": "22.8", "image_path": "train/856.png"}
{"question": "Find x", "answer": "29.1", "image_path": "train/857.png"}
{"question": "Find $x$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "6", "image_path": "train/858.png"}
{"question": "Find $m \\angle 2$.", "answer": "52", "image_path": "train/859.png"}
{"question": "Quadrilateral WXYZ is a rectangle. If $XZ = 2c$ and $ZY = 6$, and $XY = 8$, find $WY$.", "answer": "10", "image_path": "train/860.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "50", "image_path": "train/861.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram.", "answer": "20", "image_path": "train/862.png"}
{"question": "Find x", "answer": "45", "image_path": "train/863.png"}
{"question": "Find $h$ in the triangle.", "answer": "3 \\sqrt 2", "image_path": "train/864.png"}
{"question": "Find $x$. Round to the nearest tenth.", "answer": "4.8", "image_path": "train/865.png"}
{"question": "Find $DB$.", "answer": "9.2", "image_path": "train/866.png"}
{"question": "Use parallelogram ABCD to find $m\\angle DAC$", "answer": "72", "image_path": "train/867.png"}
{"question": "Quadrilateral ABCD is a rectangle. Find x", "answer": "5", "image_path": "train/868.png"}
{"question": "Find x.", "answer": "48", "image_path": "train/869.png"}
{"question": "Find y.", "answer": "1", "image_path": "train/870.png"}
{"question": "In $\\odot X, A B=30, C D=30,$ and $m \\widehat{C Z}=40$\r\nFind $m\\widehat{D Z}$", "answer": "40", "image_path": "train/871.png"}
{"question": "Find $m \\angle 1$.", "answer": "65", "image_path": "train/872.png"}
{"question": "Refer to the figure at the right. Find z.", "answer": "11.09", "image_path": "train/873.png"}
{"question": "$A E$ is a tangent. If $A D=12$ and $F E=18$, how long is $A E$ to the nearest tenth unit?", "answer": "27.5", "image_path": "train/874.png"}
{"question": "Find $\\angle V$", "answer": "46", "image_path": "train/875.png"}
{"question": "Find $m\\angle J$", "answer": "112", "image_path": "train/876.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram", "answer": "5", "image_path": "train/877.png"}
{"question": "Find the measure of $\\angle 3$ if $m∠DGF = 53$ and $m∠AGC = 40$.", "answer": "50", "image_path": "train/878.png"}
{"question": "Find $y$.", "answer": "13", "image_path": "train/879.png"}
{"question": "WXYZ is a square. If $WT = 3$, find $ZX$", "answer": "6", "image_path": "train/880.png"}
{"question": "For trapezoid QRST, M and P are midpoints of the legs. If PM = 2x, QR = 3x, and TS = 10, find PM.", "answer": "20", "image_path": "train/881.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram.", "answer": "8", "image_path": "train/882.png"}
{"question": "$\\overline{E D}$ is tangent to $\\odot F$ at point $E .$ Find $x$", "answer": "5", "image_path": "train/883.png"}
{"question": "Use parallelogram NQRM to find NQ", "answer": "14", "image_path": "train/884.png"}
{"question": "In $\\odot Z, \\angle W Z X \\cong \\angle X Z Y, m \\angle V Z U=4 x$, $m \\angle U Z Y=2 x+24,$ and $\\overline{V Y}$ and $\\overline{W U}$ are diameters.\r\nFind $m\\widehat{W V}$", "answer": "76", "image_path": "train/885.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "374.5", "image_path": "train/886.png"}
{"question": "Find the measure of $\\angle 2$ in the figure.", "answer": "52", "image_path": "train/887.png"}
{"question": "Quadrilateral $ABDC$  is a rectangle. Find $m \\angle 5 if $ m\\angle 1 = 38$.  $", "answer": "104", "image_path": "train/888.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "170", "image_path": "train/889.png"}
{"question": "Find $m\\angle V$", "answer": "193", "image_path": "train/890.png"}
{"question": "In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\\angle 8$.", "answer": "62", "image_path": "train/891.png"}
{"question": "Find $ST$.", "answer": "5", "image_path": "train/892.png"}
{"question": "Find the perimeter of $\\triangle D E F$  if  $\\triangle D E F \\sim \\triangle G F H$.", "answer": "12.75", "image_path": "train/893.png"}
{"question": "Find ST", "answer": "\\frac { 50 } { 3 }", "image_path": "train/894.png"}
{"question": "If $\\triangle SRY \\sim \\triangle WXQ, \\overline{RT} $ is an altitude of $\\triangle SRY$, $\\overline{XV}$ is an altitude of $\\triangle WXQ, RT=5, RQ=4, QY=6$, and $Y X=2,$ find $XV$.", "answer": "4", "image_path": "train/895.png"}
{"question": "Quadrilateral $A B C D$ is inscribed in $\\odot Z$ such that $m \\angle B Z A=104, m \\widehat{C B}=94,$ and $\\overline{A B} \\| \\overline{D C} .$\r\nFind $m \\widehat{A D C}$", "answer": "162", "image_path": "train/896.png"}
{"question": "If $m \\angle 1=3 x+40$, $m \\angle 2=2(y-10)$, and $m \\angle 3=2 x+70$, find $y$.", "answer": "75", "image_path": "train/897.png"}
{"question": "Find $m \\angle 5$.", "answer": "55", "image_path": "train/898.png"}
{"question": "Find $y$.", "answer": "10", "image_path": "train/899.png"}
{"question": "The area of $▱ A B C D$ is 150 square meters. The area of $▱ F G H J$ is 54 square meters. If $▱ A B C D \\sim ▱ F G H J$, find the value of $x$.", "answer": "6", "image_path": "train/900.png"}
{"question": "$\\overline{AB}$ is tangent to the circle. Find $x$. Round to the nearest tenth.", "answer": "6.1", "image_path": "train/901.png"}
{"question": "In the figure, $m∠1 = 123$. Find the measure of $\\angle 4$.", "answer": "57", "image_path": "train/902.png"}
{"question": "In $\\odot X, A B=30, C D=30,$ and $m \\widehat{C Z}=40$\r\nFind MB", "answer": "15", "image_path": "train/903.png"}
{"question": "Find $DE$.", "answer": "7.5", "image_path": "train/904.png"}
{"question": "Quadrilateral EFGH is a rectangle. If $m\\angle FEG = 57$, find $m\\angle GEH$.", "answer": "33", "image_path": "train/905.png"}
{"question": "Find $x$.", "answer": "4", "image_path": "train/906.png"}
{"question": "If $ABCD$ is a kite, find $AB$", "answer": "5", "image_path": "train/907.png"}
{"question": "Find x", "answer": "8", "image_path": "train/908.png"}
{"question": "Use parallelogram ABCD to find $m\\angle AFB$", "answer": "131", "image_path": "train/909.png"}
{"question": "If $WZ=25.3$, $YZ=22.4$, $WZ=25.3$, find $XY$.", "answer": "22.4", "image_path": "train/910.png"}
{"question": "Find the value of the variable $y$ in the figure.", "answer": "12", "image_path": "train/911.png"}
{"question": "In $\\odot R, S U=20, Y W=20,$ and $m \\widehat{Y X}=45$.\r\nFind SV", "answer": "10", "image_path": "train/912.png"}
{"question": "parallelogram MNPQ with $m \\angle M=10 x$ and $m \\angle N=20 x$, find $\\angle Q$", "answer": "120", "image_path": "train/913.png"}
{"question": "Quadrilateral $RSTU$ is circumscribed about $\\odot J$. If the preimeter is $18$ units, find $x$.", "answer": "1.5", "image_path": "train/914.png"}
{"question": "If TR = 8, LR = 3, and RW = 6, find WS.", "answer": "10", "image_path": "train/915.png"}
{"question": "Find z.", "answer": "\\frac { 22 } { 5 }", "image_path": "train/916.png"}
{"question": "The triangle is inscribed in $\\odot D$. Find the exact circumference of $\\odot D$.", "answer": "4 \\sqrt { 13 } \\pi", "image_path": "train/917.png"}
{"question": "Find x. Round to the nearest tenth, if necessary.", "answer": "5.3", "image_path": "train/918.png"}
{"question": "Find PQ", "answer": "15", "image_path": "train/919.png"}
{"question": "Find $x$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "4", "image_path": "train/920.png"}
{"question": "Find $x$.", "answer": "58", "image_path": "train/921.png"}
{"question": "$\\overline{RS}$ bisects $\\angle VRU$. Solve for $x$.", "answer": "10", "image_path": "train/922.png"}
{"question": "Find $m \\angle 2$.", "answer": "110", "image_path": "train/923.png"}
{"question": "Find $x$", "answer": "5", "image_path": "train/924.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "3.8", "image_path": "train/925.png"}
{"question": "Find $m \\widehat {CF}$.", "answer": "80", "image_path": "train/926.png"}
{"question": "If $b=18,$ find $c$ ", "answer": "12 \\sqrt { 3 }", "image_path": "train/927.png"}
{"question": "$\\triangle FGH$ is an equilateral triangle. Find $FG$.", "answer": "19", "image_path": "train/928.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "259.8", "image_path": "train/929.png"}
{"question": "Find $y$ in the figure.", "answer": "90", "image_path": "train/930.png"}
{"question": "If $\\overline{W P}$ is a median and an angle bisector, $A P=3 y+11$, $P H=7 y-5$, $m \\angle H W P=x+12$, $m \\angle P A W=3 x-2$, and $m \\angle H W A=4 x-16$, find $x$.", "answer": "20", "image_path": "train/931.png"}
{"question": "In $\\triangle JLP$, $m \\angle JMP=3 x-6$, $JK=3y-2$, and $LK=5y-8$. If $\\overline{JM}$ is an altitude of $\\triangle JLP$, find $x$.\r\n", "answer": "32", "image_path": "train/932.png"}
{"question": "Find $\\angle 7$", "answer": "98", "image_path": "train/933.png"}
{"question": "Find the area of the figure. Round to the nearest hundredth, if necessary.", "answer": "68.6", "image_path": "train/934.png"}
{"question": "Find z", "answer": "10 \\sqrt { 2 }", "image_path": "train/935.png"}
{"question": "Find x", "answer": "117", "image_path": "train/936.png"}
{"question": "If PR || KL, KN = 9, LN = 16, PM = 2 KP, find MR  ", "answer": "40 / 3", "image_path": "train/937.png"}
{"question": "Find $m \\angle 2$.", "answer": "75", "image_path": "train/938.png"}
{"question": "Find $y$ in the figure.", "answer": "11", "image_path": "train/939.png"}
{"question": "Find $m \\angle 7$.", "answer": "53", "image_path": "train/940.png"}
{"question": "Find the value of x.", "answer": "8", "image_path": "train/941.png"}
{"question": "For the pair of similar figures, find the area of the green figure.", "answer": "81", "image_path": "train/942.png"}
{"question": "The two circles are congruent. Find $x$.", "answer": "16", "image_path": "train/943.png"}
{"question": "In parallelogram $ABCD$, $\\overline{BD}$ and $\\overline{AC}$ intersect at $E$. If $AE = 9$, $BE = 3x - 7$, and $DE = x + 5$, find $x$.", "answer": "6", "image_path": "train/944.png"}
{"question": "$\\overline{JH}, \\overline{JP},$ and $\\overline{PH}$ are midsegments of $\\triangle KLM$. Find $x$.", "answer": "60", "image_path": "train/945.png"}
{"question": "Find the measure of $x$.", "answer": "0.5", "image_path": "train/946.png"}
{"question": "$m∠19 = 100 + 20x$, $m∠20 = 20x $. Find the measure of $\\angle 19$.", "answer": "140", "image_path": "train/947.png"}
{"question": "find cos B", "answer": "\\frac { 5 } { 7 }", "image_path": "train/948.png"}
{"question": "$\\overline{XY}$ and $\\overline{XZ}$ are midsegments of $\\triangle RST$. Find $XZ$.", "answer": "6.5", "image_path": "train/949.png"}
{"question": "Find $m\\angle Z X Y$", "answer": "65", "image_path": "train/950.png"}
{"question": "Find $m \\angle 1$.", "answer": "66", "image_path": "train/951.png"}
{"question": "Find the perimeter of the given triangle. $\\triangle A B C,$ if $\\triangle A B C \\sim \\triangle C B D, C D=4$, $D B=3,$ and $C B=5$.", "answer": "20", "image_path": "train/952.png"}
{"question": "Find the perimeter of quadrilateral ABCD.", "answer": "40 + 14 \\sqrt { 2 }", "image_path": "train/953.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram.", "answer": "12", "image_path": "train/954.png"}
{"question": "Find $x$.", "answer": "12", "image_path": "train/955.png"}
{"question": "Find DE", "answer": "6", "image_path": "train/956.png"}
{"question": "$\\triangle PQS \\cong \\triangle RQS$. Find $x$.", "answer": "16", "image_path": "train/957.png"}
{"question": "Chords $\\overline{A C}$ and $\\overline{D F}$ are equidistant from the center. If the radius of $\\odot G$ is 26 find $D E$", "answer": "24", "image_path": "train/958.png"}
{"question": "Find $x$.", "answer": "19", "image_path": "train/959.png"}
{"question": "Find the area of the figure. Round to the nearest tenth.", "answer": "129.9", "image_path": "train/960.png"}
{"question": "Find $h$.", "answer": "15 \\sqrt 3", "image_path": "train/961.png"}
{"question": "Find $m\\angle 2$", "answer": "130", "image_path": "train/962.png"}
{"question": "Find $JL$.", "answer": "12", "image_path": "train/963.png"}
{"question": "Find x. Round to the nearest tenth.", "answer": "57.2", "image_path": "train/964.png"}
{"question": "isosceles trapezoid TWYZ with $\\angle Z \\cong \\angle Y, m \\angle Z=30 x$, $\\angle T \\cong \\angle W,$ and $m \\angle T=20 x$, find $\\angle W$", "answer": "72", "image_path": "train/965.png"}
{"question": "Express the ratio of $\\tan B$ as a decimal to the nearest hundredth.", "answer": "2.40", "image_path": "train/966.png"}
{"question": "Find $CB$.", "answer": "15", "image_path": "train/967.png"}
{"question": "Find x.", "answer": "2 \\sqrt { 10 }", "image_path": "train/968.png"}
{"question": "If $\\frac{I J}{X J}=\\frac{HJ}{YJ}, m \\angle W X J=130$, and $m \\angle WZG=20,$ find $m \\angle JHG$", "answer": "110", "image_path": "train/969.png"}
{"question": "Quadrilateral $ABCD$ is a rhombus. If $m\\angle BCD = 54$, find $m\\angle BAC$.", "answer": "27", "image_path": "train/970.png"}
{"question": "Polygon $BCDE$ $\\cong$ polygon $RSTU$. Find $y$.", "answer": "42", "image_path": "train/971.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "70", "image_path": "train/972.png"}
{"question": "Find $x$.", "answer": "13", "image_path": "train/973.png"}
{"question": "In the figure, $m ∠1 = 53$. Find the measure of $∠3$.", "answer": "53", "image_path": "train/974.png"}
{"question": "Solve for $x$.", "answer": "15", "image_path": "train/975.png"}
{"question": "Find $m\\angle C$", "answer": "128", "image_path": "train/976.png"}
{"question": "Find x", "answer": "6", "image_path": "train/977.png"}
{"question": "Find the perimeter of the triangle. Round to the nearest hundredth.", "answer": "28.52", "image_path": "train/978.png"}
{"question": " $m \\widehat{G H}=78$ Find $m\\angle 1$", "answer": "39", "image_path": "train/979.png"}
{"question": "Quadrilateral WXYZ is a rectangle. If $XW = 3$, $WZ = 4$, and $XZ = b$, find $YW$. ", "answer": "5", "image_path": "train/980.png"}
{"question": "Find $y$.", "answer": "2", "image_path": "train/981.png"}
{"question": "Find $z$.", "answer": "10 \\sqrt { 5 }", "image_path": "train/982.png"}
{"question": "Find $m\\angle 2$.", "answer": "151", "image_path": "train/983.png"}
{"question": "Use parallelogram to  find $y$", "answer": "17", "image_path": "train/984.png"}
{"question": "Find $JM$.", "answer": "5.5", "image_path": "train/985.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "19.2", "image_path": "train/986.png"}
{"question": "Use parallelogram WXYZ to find $m\\angle WZY$", "answer": "75", "image_path": "train/987.png"}
{"question": "Find the perimeter of $\\triangle D E F,$ if $\\triangle D E F \\sim \\triangle A C B$", "answer": "42", "image_path": "train/988.png"}
{"question": "Find $x$.", "answer": "15", "image_path": "train/989.png"}
{"question": "Find the area of the figure. Round to the nearest tenth.", "answer": "474", "image_path": "train/990.png"}
{"question": "If $m \\angle S=3x$ and $m \\angle V=x+16$, find $m \\angle S$.", "answer": "24", "image_path": "train/991.png"}
{"question": "Find the value of $x$ in each diagram", "answer": "52", "image_path": "train/992.png"}
{"question": "Find $BE$.", "answer": "2.1", "image_path": "train/993.png"}
{"question": "Find $m \\angle S$.", "answer": "66", "image_path": "train/994.png"}
{"question": "Use rectangle LMNP, parallelogram LKMJ to solve the problem.\r\nIf $M K=6 x, K L=3 x+2 y,$ and $J N=14-x$\r\nfind $y$", "answer": "3", "image_path": "train/995.png"}
{"question": "Find $E H$ if $\\triangle A B C \\sim \\triangle D E F, \\overline{B G}$ is an altitude of $\\triangle A B C, \\overline{E H}$ is an altitude of $\\triangle D E F, B G=3$, $B F=4, F C=2,$ and $C E=1$", "answer": "\\frac { 3 } { 2 }", "image_path": "train/996.png"}
{"question": "In the figure, $ m ∠1 = 3a + 40 $, $ m ∠2 = 2a + 25 $, and $ m ∠3 = 5b - 26 $. Find $b$.", "answer": "27", "image_path": "train/997.png"}
{"question": "Find y", "answer": "10", "image_path": "train/998.png"}
{"question": "Quadrilateral ABCD is a rectangle. $m\\angle 2 = 40$. Find $m \\angle 7$", "answer": "40", "image_path": "train/999.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "2.37", "image_path": "train/1000.png"}
{"question": "Find x.", "answer": "7 \\sqrt { 3 }", "image_path": "train/1001.png"}
{"question": "find $sinR$", "answer": "0.8", "image_path": "train/1002.png"}
{"question": "Find x. Round to the nearest degree.", "answer": "122", "image_path": "train/1003.png"}
{"question": "Find x", "answer": "2 \\sqrt { 21 }", "image_path": "train/1004.png"}
{"question": "Find y.", "answer": "5 \\sqrt { 3 }", "image_path": "train/1005.png"}
{"question": "Find x", "answer": "\\frac { 19 \\sqrt { 2 } } { 2 }", "image_path": "train/1006.png"}
{"question": "Polygon ABCD ~ polygon AEFG, $m\\angle AGF = 108$, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26.\r\nFind the perimeter of trapezoid AEFG", "answer": "45.75", "image_path": "train/1007.png"}
{"question": "Find $y$.", "answer": "2", "image_path": "train/1008.png"}
{"question": "Find $\\angle 6$.", "answer": "123", "image_path": "train/1009.png"}
{"question": "Use parallelogram NQRM to find x", "answer": "4", "image_path": "train/1010.png"}
{"question": "Quadrilateral JKLM is a rectangle. If $m\\angle KJL = 2x + 4$ and $m\\angle JLK = 7x + 5$, find $x$.", "answer": "9", "image_path": "train/1011.png"}
{"question": "$m \\angle BAC=40, m \\angle DAC=40,$ and $DC=10,$ find $BC$.", "answer": "10", "image_path": "train/1012.png"}
{"question": "Find the area of $ \\triangle JKM$.", "answer": "21", "image_path": "train/1013.png"}
{"question": "Find x.", "answer": "34", "image_path": "train/1014.png"}
{"question": "in $\\triangle XYZ$, $P$ is the centroid, $KP=3$, and $XJ=8$. Find $XK$.", "answer": "9", "image_path": "train/1015.png"}
{"question": "Find the variable of $x$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "7.1", "image_path": "train/1016.png"}
{"question": "Find the perimeter of the figure. Round to the nearest tenth if necessary.", "answer": "54.8", "image_path": "train/1017.png"}
{"question": "If $m \\widehat{B C}=30$ and $\\overline{A B} \\cong \\widehat{C D},$ find $m \\widehat{A B}$", "answer": "75", "image_path": "train/1018.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "10", "image_path": "train/1019.png"}
{"question": "In $\\odot D, \\overline{D E} \\cong \\overline{E C}, m \\widehat{C F}=60,$ and\r\n$\\overline{D E} \\perp \\overline{E C} .$ Find $m \\widehat{A F}$", "answer": "120", "image_path": "train/1020.png"}
{"question": "Find the perimeter of each polygon for the given information.", "answer": "60", "image_path": "train/1021.png"}
{"question": "Find $x$. Round to the nearest tenth.", "answer": "44.0", "image_path": "train/1022.png"}
{"question": "Find x. Round to the nearest degree.", "answer": "28", "image_path": "train/1023.png"}
{"question": "Find the area of the shaded region. Assume that the polygon is regular unless otherwise stated. Round to the nearest tenth.", "answer": "42.1", "image_path": "train/1024.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "3", "image_path": "train/1025.png"}
{"question": "Find $m\\angle Z$ in the trapezoid", "answer": "68", "image_path": "train/1026.png"}
{"question": "Quadrilateral $WXYZ$ is inscribed in $\\odot V$. Find $m \\angle Y$.", "answer": "85", "image_path": "train/1027.png"}
{"question": "Circle $O$ has a radius of $10, A B=10$ and $m \\overrightarrow{A B}=60 .$ Find $m\\widehat{A X}$", "answer": "5", "image_path": "train/1028.png"}
{"question": "Find $x$. Round to the nearest tenth.", "answer": "12.7", "image_path": "train/1029.png"}
{"question": "For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure.", "answer": "\\frac { 5 } { 2 }", "image_path": "train/1030.png"}
{"question": "Find x.", "answer": "5", "image_path": "train/1031.png"}
{"question": "$ \\triangle WXY $  and $ \\triangle XYZ $ are isosceles and $m∠XYZ = 128$. Find the measure of $∠WXY$.", "answer": "76", "image_path": "train/1032.png"}
{"question": "Find $m \\angle 3$.", "answer": "51", "image_path": "train/1033.png"}
{"question": "Find $m \\angle W$.", "answer": "74", "image_path": "train/1034.png"}
{"question": "Find the area of the figure. Round to the nearest tenth.", "answer": "91.2", "image_path": "train/1035.png"}
{"question": "What is $m∠EFG$?", "answer": "70", "image_path": "train/1036.png"}
{"question": "Find the area of the circle. Round to the nearest tenth.", "answer": "113.1", "image_path": "train/1037.png"}
{"question": "Find $\\widehat{D G}$ if $m \\angle D G I=24$ and $r=6$", "answer": "\\frac { 22 } { 5 } \\pi", "image_path": "train/1038.png"}
{"question": "A plane travels from Des Moines to Phoenix, on to Atlanta, and back to Des Moines, as shown below. Find the distance in miles from  Atlanta to Des Moines if the total trip was 3482 miles.", "answer": "738", "image_path": "train/1039.png"}
{"question": "For trapezoid $Q R S T, A$ and $B$ are midpoints of the legs. Find $m \\angle Q$", "answer": "60", "image_path": "train/1040.png"}
{"question": "Find y.", "answer": "\\sqrt { 510 }", "image_path": "train/1041.png"}
{"question": "Find the area of the shaded region. Assume the inscribed polygon is regular.", "answer": "3.3", "image_path": "train/1042.png"}
{"question": "Find $AC$ if $\\triangle ABC$ is an isosceles triangle with $\\overline{AB} \\cong \\overline{BC}$. ", "answer": "4", "image_path": "train/1043.png"}
{"question": "$\\overline{PM}$ is a diameter of $\\odot R$. Find $m \\widehat {MNQ}$.", "answer": "295", "image_path": "train/1044.png"}
{"question": "Find the angle measure of $\\angle3$.", "answer": "90", "image_path": "train/1045.png"}
{"question": "Find AE", "answer": "8", "image_path": "train/1046.png"}
{"question": "Find y", "answer": "12 \\sqrt { 2 }", "image_path": "train/1047.png"}
{"question": "Find SC", "answer": "21", "image_path": "train/1048.png"}
{"question": "Use parallelogram ABCD to find AF", "answer": "6.86", "image_path": "train/1049.png"}
{"question": "Find x. Round the angle measure to the nearest degree", "answer": "112", "image_path": "train/1050.png"}
{"question": "Find the circumference of $\\odot A$.", "answer": "20 \\pi", "image_path": "train/1051.png"}
{"question": "Find the measure of $m\\angle 3$. Assume that segments that appear\r\ntangent are tangent.", "answer": "26", "image_path": "train/1052.png"}
{"question": "Find the value of the variable $x$ in the figure.", "answer": "40", "image_path": "train/1053.png"}
{"question": "Find the measure of $\\angle P$", "answer": "61", "image_path": "train/1054.png"}
{"question": "Find z.", "answer": "12 \\sqrt { 3 }", "image_path": "train/1055.png"}
{"question": "$a=8, b=15,$ and $c=17$ find $tanA$", "answer": "0.53", "image_path": "train/1056.png"}
{"question": "In the figure, $m∠4 = 104$, $m∠14 = 118$. Find the measure of $\\angle 10$.", "answer": "118", "image_path": "train/1057.png"}
{"question": "Find the perimeter of the triangle. Round to the nearest tenth if necessary.", "answer": "48", "image_path": "train/1058.png"}
{"question": "In $\\odot P$, the diameter is $9$, find the length of $\\widehat {QT}$. Round to the nearest hundredth.", "answer": "8.80", "image_path": "train/1059.png"}
{"question": "Find $m\\angle 1$", "answer": "48", "image_path": "train/1060.png"}
{"question": "Find $x$ so that the quadrilateral is a parallelogram.", "answer": "2", "image_path": "train/1061.png"}
{"question": "Find x", "answer": "235", "image_path": "train/1062.png"}
{"question": "Find the area of the regular polygon. Round to the nearest tenth.", "answer": "237.8", "image_path": "train/1063.png"}
{"question": "Find AE", "answer": "4", "image_path": "train/1064.png"}
{"question": "The diameters of $\\odot A, \\odot B,$ and $\\odot C$ are 10 inches,\r\n20 inches, and 14 inches, respectively.\r\nFind BY", "answer": "3", "image_path": "train/1065.png"}
{"question": "Quadrilateral MNOP is a rhombus. Find $m\\angle MRN $", "answer": "90", "image_path": "train/1066.png"}
{"question": "The segment is tangent to the circle. Find $x$.", "answer": "9", "image_path": "train/1067.png"}
{"question": "Find $C D$ if $A E=8, E D=4,$ and $B E=6$", "answer": "9", "image_path": "train/1068.png"}
{"question": "Find the area of the triangle.", "answer": "167.2", "image_path": "train/1069.png"}
{"question": "Find $m\\angle E$", "answer": "78", "image_path": "train/1070.png"}
{"question": "If $\\overline{E C}$ is an altitude of $\\triangle A E D, m \\angle 1=2 x+7,$ and $m \\angle 2=3 x+13,$ find $m \\angle 2$.", "answer": "55", "image_path": "train/1071.png"}
{"question": "Find x.", "answer": "3 \\sqrt { 2 }", "image_path": "train/1072.png"}
{"question": "Find $m\\angle A$", "answer": "122", "image_path": "train/1073.png"}
{"question": "Find x", "answer": "6.75", "image_path": "train/1074.png"}
{"question": "Find y", "answer": "6 \\sqrt { 42 }", "image_path": "train/1075.png"}
{"question": "In the figure, $\\overline{FJ} \\cong \\overline{FH}$ and $\\overline{GF} \\cong \\overline{GH}$. If $m∠GHJ=152$ and  $m∠G=32$, find $m∠JFH$.", "answer": "24", "image_path": "train/1076.png"}
{"question": "Find x", "answer": "7", "image_path": "train/1077.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "156", "image_path": "train/1078.png"}
{"question": "Find x", "answer": "8", "image_path": "train/1079.png"}
{"question": "Find $y$.", "answer": "17", "image_path": "train/1080.png"}
{"question": "Find $x$.", "answer": "5.4", "image_path": "train/1081.png"}
{"question": "For isosceles trapezoid $X Y Z W$ find the length of the median", "answer": "14", "image_path": "train/1082.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "128.1", "image_path": "train/1083.png"}
{"question": "Find the measure of $\\angle 3$.", "answer": "49", "image_path": "train/1084.png"}
{"question": "$\\triangle LMN \\cong \\triangle QRS$. Find $y$.", "answer": "50", "image_path": "train/1085.png"}
{"question": "Find the area of the shaded region. Assume that the triangle is equilateral.", "answer": "29.5", "image_path": "train/1086.png"}
{"question": "Triangles $F G H$ and $F H J$ are inscribed in $\\odot K$ with $\\widehat{F G} \\cong \\widehat{F I} .$ Find $x$ if $m \\angle 1=6 x-5,$ and $m \\angle 2=7 x+4$", "answer": "7", "image_path": "train/1087.png"}
{"question": "Use parallelogram $ABCD$ to find the measure of $m\\angle ADC$", "answer": "65", "image_path": "train/1088.png"}
{"question": "Find the measure of $∠T$ to the nearest tenth.", "answer": "28.5", "image_path": "train/1089.png"}
{"question": "Find $m \\widehat {RT}$.", "answer": "126", "image_path": "train/1090.png"}
{"question": "Find the perimeter of the $\\triangle DEF$, if $\\triangle DEF \\sim \\triangle CBF$, perimeter of $\\triangle CBF=27, DF=6, FC=8$.", "answer": "20.25", "image_path": "train/1091.png"}
{"question": "What is the value of x in the figure below? Round to the nearest tenth.", "answer": "11.1", "image_path": "train/1092.png"}
{"question": "$MC=7,RM=4$, and $AT=16$. Find $RB$.", "answer": "12", "image_path": "train/1093.png"}
{"question": "Find the measure of the altitude drawn to the hypotenuse.", "answer": "\\sqrt { 297 }", "image_path": "train/1094.png"}
{"question": "Find the perimeter of the parallelogram.", "answer": "96", "image_path": "train/1095.png"}
{"question": "Find $DB$.", "answer": "5", "image_path": "train/1096.png"}
{"question": "Find y.", "answer": "8 \\sqrt { 2 }", "image_path": "train/1097.png"}
{"question": "Find x. Round the angle measure to the nearest degree.", "answer": "48", "image_path": "train/1098.png"}
{"question": "Find the variable of $x$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "14.6", "image_path": "train/1099.png"}
{"question": "Find the area of the trapezoid.", "answer": "273", "image_path": "train/1100.png"}
{"question": "Refer to trapezoid $CDFG$ with median $\\overline{HE}$. Let $\\overline{YZ}$ be the median of $HEFG$. Find $YZ$.", "answer": "34", "image_path": "train/1101.png"}
{"question": "Use the figure to find the indicated variable. If $m \\angle 4 = 2x - 17$ and $m \\angle 1 = 85$, find $x$.", "answer": "56", "image_path": "train/1102.png"}
{"question": "If $m∠2 = 4x + 7$ and $m∠7 = 5x - 13$, find $x$.", "answer": "20", "image_path": "train/1103.png"}
{"question": "Find the value of x.", "answer": "45", "image_path": "train/1104.png"}
{"question": "$m \\widehat{J H}=114$ Find $m\\angle 3$", "answer": "33", "image_path": "train/1105.png"}
{"question": "Find x. Round to the nearest tenth if necessary.", "answer": "2", "image_path": "train/1106.png"}
{"question": "In the figure, $LH$ is the midsegment of trapezoid $FGJK$. What is the value of $x$ ?", "answer": "11.8", "image_path": "train/1107.png"}
{"question": "Find the area of the shaded region.", "answer": "50.3", "image_path": "train/1108.png"}
{"question": "Find x.", "answer": "\\sqrt { 141 }", "image_path": "train/1109.png"}
{"question": "Find the perimeter or circumference of the figure. Round to the nearest tenth.", "answer": "16", "image_path": "train/1110.png"}
{"question": "Find $x$.", "answer": "10", "image_path": "train/1111.png"}
{"question": "Refer to the figure at the right. Find the value of $m ∠BCE$ if $ p \\parallel q $.", "answer": "75", "image_path": "train/1112.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth.", "answer": "37.4", "image_path": "train/1113.png"}
{"question": "Find the perimeter of $▱ JKLM$.", "answer": "22.4", "image_path": "train/1114.png"}
{"question": "find sin A", "answer": "\\frac { 5 } { 7 }", "image_path": "train/1115.png"}
{"question": "Find the measure of $∠T$ to the nearest tenth.", "answer": "56.4", "image_path": "train/1116.png"}
{"question": "Find the perimeter of the parallelogram.", "answer": "76", "image_path": "train/1117.png"}
{"question": "Find the measure of $∠R$ to the nearest tenth.", "answer": "39.6", "image_path": "train/1118.png"}
{"question": "$\\triangle MHJ \\cong \\triangle PQJ$. Find $y$.", "answer": "5", "image_path": "train/1119.png"}
{"question": "In $\\triangle ACE$, $P$ is the centroid. $PF=6$ and $AD=15$. Find $AP$.", "answer": "10", "image_path": "train/1120.png"}
{"question": "Find the area of the figure. Round to the nearest tenth.", "answer": "374", "image_path": "train/1121.png"}
{"question": "Find z ", "answer": "4 \\sqrt { 3 }", "image_path": "train/1122.png"}
{"question": "In the figure, $m∠1 = 50$ and $m∠3 = 60$. Find the measure of $\\angle 5$.", "answer": "60", "image_path": "train/1123.png"}
{"question": "Find x", "answer": "41.8", "image_path": "train/1124.png"}
{"question": "Use parallelogram ABCD to find $y $", "answer": "11", "image_path": "train/1125.png"}
{"question": "Find the value of $d$ in the parallelogram", "answer": "42", "image_path": "train/1126.png"}
{"question": "Find y.", "answer": "15", "image_path": "train/1127.png"}
{"question": "Solve for $x$.", "answer": "12", "image_path": "train/1128.png"}
{"question": "In the figure, $m∠3 = 43$. Find the measure of $\\angle 13$.", "answer": "43", "image_path": "train/1129.png"}
{"question": "Find x", "answer": "35", "image_path": "train/1130.png"}
{"question": "In $\\triangle PQR$, $ZQ=3a-11$, $ZP=a+5$, $PY=2 c-1$, $YR=4 c-11$, $m \\angle PRZ=4 b-17$, $m \\angle ZRQ=3 b-4$, $m \\angle QYR=7 b+6$, and $m \\angle PXR=2 a+10$.  Find $PR$ if $\\overline{QY}$ is a median.", "answer": "18", "image_path": "train/1131.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth.", "answer": "66.3", "image_path": "train/1132.png"}
{"question": "What is the circumference of $\\odot T$? Round to the nearest tenth.", "answer": "40.8", "image_path": "train/1133.png"}
{"question": "Use parallelogram to find $a$", "answer": "7", "image_path": "train/1134.png"}
{"question": "In $\\odot F, \\overline{F H} \\cong \\overline{F L}$ and $\\mathrm{FK}=17$.\r\nFind LK", "answer": "15", "image_path": "train/1135.png"}
{"question": "In the figure, $\\triangle FGH$ is a right triangle with hypotenuse $\\overline{FH}$ and $GJ = GH$. What is the measure of $∠JGH$?", "answer": "56", "image_path": "train/1136.png"}
{"question": "The area of trapezoid $JKLM$ is 138 square feet. The area of trapezoid $QRST$ is 5.52 square feet. If trapezoid $J K L M$ $ \\sim$ trapezoid $QRST$, find the scale factor from trapezoid $JKLM$ to trapezoid $QRST$.", "answer": "5", "image_path": "train/1137.png"}
{"question": "If $A D=8, A E=12,$ and $E C=18,$ find $A B$", "answer": "20", "image_path": "train/1138.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth.", "answer": "53.5", "image_path": "train/1139.png"}
{"question": "Find $x$.", "answer": "6", "image_path": "train/1140.png"}
{"question": "Find $x$ in $\\triangle P Q R$", "answer": "2 \\sqrt { 6 }", "image_path": "train/1141.png"}
{"question": "Find the length of $AB$ in the isosceles triangle $ABC$. ", "answer": "12.5", "image_path": "train/1142.png"}
{"question": "Find the measure of $\\angle 3$.", "answer": "147", "image_path": "train/1143.png"}
{"question": "Find $m \\widehat{JK}$.", "answer": "56", "image_path": "train/1144.png"}
{"question": "Use rectangle LMNP, parallelogram LKMJ to solve the problem.\r\nIf $m \\angle P L K=110,$ find $m \\angle L K M$", "answer": "140", "image_path": "train/1145.png"}
{"question": "The segment is tangent to the circle. Find $x$.", "answer": "8", "image_path": "train/1146.png"}
{"question": "Chords $\\overline{JF}$ and $\\overline{BC}$ intersect at $K .$ If $B K=8$, $K C=12,$ and $K F=16,$ find $J K$", "answer": "6", "image_path": "train/1147.png"}
{"question": "find tan A", "answer": "\\frac { 15 } { 16 }", "image_path": "train/1148.png"}
{"question": "Use parallelogram PQRS to find $QR$", "answer": "3", "image_path": "train/1149.png"}
{"question": "RSTV is a trapezoid with bases $\\overline{R V}$ and $\\overline{S T}$ and median $\\overline{M N}$. Find $x$ if $M N=60, S T=4 x-1,$ and $R V=6 x+11$", "answer": "11", "image_path": "train/1150.png"}
{"question": "In $\\odot F$, $GK=14$ and $m \\widehat{GHK}=142$. Find $m \\widehat {GH}$.", "answer": "71", "image_path": "train/1151.png"}
{"question": "Find x.", "answer": "8 \\sqrt { 3 }", "image_path": "train/1152.png"}
{"question": "Each pair of polygons is similar. Find x.", "answer": "91", "image_path": "train/1153.png"}
{"question": "Find $x$ in each figure.", "answer": "13", "image_path": "train/1154.png"}
{"question": "Find the area of the rhombus.", "answer": "60", "image_path": "train/1155.png"}
{"question": "Find y.", "answer": "20", "image_path": "train/1156.png"}
{"question": "Find $m \\angle 4$.", "answer": "40", "image_path": "train/1157.png"}
{"question": "Quadrilateral ABCD is a rhombus. If $m\\angle BCD = 120$, find $m\\angle DAC$.", "answer": "60", "image_path": "train/1158.png"}
{"question": "Find $y$ so that $\\overline{BE}$ and $\\overline{AD}$ are perpendicular.", "answer": "8.3", "image_path": "train/1159.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "80", "image_path": "train/1160.png"}
{"question": "If $A N$ is 5 meters long, find the exact circumference of $\\odot N .$", "answer": "10 \\pi", "image_path": "train/1161.png"}
{"question": "In the figure, $m∠1 = 94$. Find the measure of $\\angle 3$.", "answer": "94", "image_path": "train/1162.png"}
{"question": "In the figure, $QR \\| TS$, $QT \\| RS$, and $m \\angle 1=131$. Find the measure of $\\angle 4$. ", "answer": "49", "image_path": "train/1163.png"}
{"question": "Circle $O$ has a radius of $10, A B=10$ and $m \\overrightarrow{A B}=60 .$ Find $m\\widehat{O X}$", "answer": "5 \\sqrt { 3 }", "image_path": "train/1164.png"}
{"question": "Each pair of polygons is similar. Find y.", "answer": "30", "image_path": "train/1165.png"}
{"question": "Find x", "answer": "8 \\sqrt { 41 }", "image_path": "train/1166.png"}
{"question": "Express the ratio of $\\tan A$ as a decimal to the nearest hundredth.", "answer": "1.33", "image_path": "train/1167.png"}
{"question": "In A, the radius is $14$ and $CD = 22$. Find $EB$. Round to the nearest hundredth.", "answer": "5.34", "image_path": "train/1168.png"}
{"question": "Find $x$.", "answer": "70", "image_path": "train/1169.png"}
{"question": "$\\overline{HK}$ and $\\overline{IG}$ are diameters of $\\odot L$. Find $m \\widehat {HGK}$.", "answer": "180", "image_path": "train/1170.png"}
{"question": "If $\\angle R S T$ is a right angle, $\\overline{SU} \\perp \\overline{RT}$, $\\overline{UV} \\perp \\overline{ST},$ and $m \\angle RT S=47,$ find $m \\angle R$", "answer": "43", "image_path": "train/1171.png"}
{"question": "Find $x$ if $\\overline{AD}$ is a median of $\\triangle ABC$.", "answer": "5", "image_path": "train/1172.png"}
{"question": "Use parallelogram MNPR to find $y$", "answer": "6.45", "image_path": "train/1173.png"}
{"question": "Find x.", "answer": "6 \\sqrt { 3 }", "image_path": "train/1174.png"}
{"question": "Find the area of the figure. Round to the nearest tenth, if necessary.", "answer": "1050", "image_path": "train/1175.png"}
{"question": "Find the perimeter of $\\triangle P Q R,$ if $\\triangle P Q M \\sim \\triangle P R Q$\r\n", "answer": "78", "image_path": "train/1176.png"}
{"question": "Find the circumference of the figure. Round to the nearest tenth.", "answer": "18.8", "image_path": "train/1177.png"}
{"question": "Find x.", "answer": "35", "image_path": "train/1178.png"}
{"question": "Find $x$. $A = 92$ in$^2$.", "answer": "8.4", "image_path": "train/1179.png"}
{"question": "The diameter of $\\odot S$ is $30$ units, the diameter of $\\odot R$ is $20$ units, and $DS=9$ units. Find $CD$.", "answer": "6", "image_path": "train/1180.png"}
{"question": "In the figure, $m ∠1 = 53$. Find the measure of $∠5$.", "answer": "127", "image_path": "train/1181.png"}
{"question": "In the figure, $QR \\| TS$, $QT \\| RS$, and $m \\angle 1=131$. Find the measure of $\\angle 8$. ", "answer": "131", "image_path": "train/1182.png"}
{"question": "Find the perimeter of the figure. Round to the nearest hundredth, if necessary.", "answer": "37.9", "image_path": "train/1183.png"}
{"question": "Find the area of the kite.", "answer": "60", "image_path": "train/1184.png"}
{"question": "Find $m\\angle 1$.", "answer": "59", "image_path": "train/1185.png"}
{"question": "Express the ratio of $\\tan V$ as a decimal to the nearest hundredth.", "answer": "0.29", "image_path": "train/1186.png"}
{"question": "For trapezoid QRTU, V and S are midpoints of the legs. If VS = 9 and UT = 12, find QR.", "answer": "7", "image_path": "train/1187.png"}
{"question": "Find $m\\angle Q$", "answer": "121", "image_path": "train/1188.png"}
{"question": "Refer to the triangle shown below. Find $x$ to the nearest tenth.", "answer": "10", "image_path": "train/1189.png"}
{"question": "$a=14, b=48,$ and $c=50$, find $sinB$", "answer": "0.96", "image_path": "train/1190.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "155.5", "image_path": "train/1191.png"}
{"question": "Find QX if $E X=24$ and $D E=7$", "answer": "18", "image_path": "train/1192.png"}
{"question": "Find $x$. $A = 104$ ft$^2$.", "answer": "6.3", "image_path": "train/1193.png"}
{"question": "Find y.", "answer": "10", "image_path": "train/1194.png"}
{"question": "Find $x$. (Hint: Draw an auxiliary line.)", "answer": "22", "image_path": "train/1195.png"}
{"question": "Find x to the nearest tenth.", "answer": "9.67", "image_path": "train/1196.png"}
{"question": "In $\\odot A, m \\angle E A D=42$. Find $m \\widehat{C B E}$", "answer": "180", "image_path": "train/1197.png"}
{"question": "Use parallelogram JKLM to find $a$ if $J K=2 b+3$ and $J M=3 a$.", "answer": "7", "image_path": "train/1198.png"}
{"question": "Find $x$.", "answer": "45", "image_path": "train/1199.png"}
{"question": "Find $m \\angle 6$.", "answer": "49", "image_path": "train/1200.png"}
{"question": "Quadrilateral MNOP is a rhombus. If PR = 12, find RN.", "answer": "12", "image_path": "train/1201.png"}
{"question": "Solve for $x$.", "answer": "5", "image_path": "train/1202.png"}
{"question": "Find $m \\angle X$", "answer": "117", "image_path": "train/1203.png"}
{"question": "Find y.", "answer": "1.5", "image_path": "train/1204.png"}
{"question": "Circle $W$ has a radius of 4 units, $\\odot Z$ has a radius of 7 units, and $X Y=2 .$ Find $I C$", "answer": "20", "image_path": "train/1205.png"}
{"question": "$\\triangle RSV \\cong \\triangle TVS$. Find $y$.", "answer": "12.5", "image_path": "train/1206.png"}
{"question": "Find $x$.", "answer": "9", "image_path": "train/1207.png"}
{"question": "Find $m∠1$.", "answer": "67", "image_path": "train/1208.png"}
{"question": "Find $x$.", "answer": "20", "image_path": "train/1209.png"}
{"question": "Find the length of $XY$", "answer": "9", "image_path": "train/1210.png"}
{"question": "If $\\overline{PQ} \\cong \\overline{UQ}$, $\\overline{PR} \\cong \\overline{RT}$ and $ m ∠ PQU = 40 $, find $ m ∠R $.", "answer": "40", "image_path": "train/1211.png"}
{"question": "Find the variable of $c$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "22.8", "image_path": "train/1212.png"}
{"question": "Find $m\\angle F$", "answer": "116", "image_path": "train/1213.png"}
{"question": "If $A B=60$ and $D E=48,$ find $C F$", "answer": "18", "image_path": "train/1214.png"}
{"question": "Find z.", "answer": "6 \\sqrt { 3 }", "image_path": "train/1215.png"}
{"question": "Find $QR$ if $\\triangle QRS$ is an equilateral triangle.", "answer": "2", "image_path": "train/1216.png"}
{"question": "Find the value of the variable $x$ in the figure.", "answer": "63", "image_path": "train/1217.png"}
{"question": "Find the area of $▱ ABCD$.", "answer": "50", "image_path": "train/1218.png"}
{"question": "Polygon ABCD ~ polygon AEFG, $m\\angle AGF = 108$, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26.\r\nFind scale factor of trapezoid ABCD to trapezoid AEFG", "answer": "1.6", "image_path": "train/1219.png"}
{"question": "$ABCD$ is a rhombus. If $PB = 12$, $AB = 15$, and $m\\angle ABD = 24$. Find $m\\angle ACB$", "answer": "66", "image_path": "train/1220.png"}
{"question": "Find $B C$ if $B E=24, C D=32,$ and $A B=33$", "answer": "11", "image_path": "train/1221.png"}
{"question": "Find $y$ in $\\triangle P Q R$", "answer": "2 \\sqrt { 3 }", "image_path": "train/1222.png"}
{"question": "A square with 5-centimeter sides is inscribed in a circle. What is the circumference of the circle? Round your answer to the nearest\r\ntenth of a centimeter.", "answer": "22.2", "image_path": "train/1223.png"}
{"question": "In $\\Delta G H J$, $H P=5 x-16$, $P J=3 x+8$, $m \\angle G J N=6 y-3$, $m \\angle N J H=4 y+23$ and $m \\angle H M G=4 z+14$. If $\\overline{HM}$ is an altitude of $∠GHJ$, find the value of $z$.", "answer": "19", "image_path": "train/1224.png"}
{"question": "Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "7.4", "image_path": "train/1225.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth, if necessary.", "answer": "333.9", "image_path": "train/1226.png"}
{"question": "In $\\odot F, \\overline{F H} \\cong \\overline{F L}$ and $\\mathrm{FK}=17$.\r\nFind JH", "answer": "15", "image_path": "train/1227.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth.", "answer": "77.0", "image_path": "train/1228.png"}
{"question": "Find the area of the circle. Round to the nearest tenth.", "answer": "38707.6", "image_path": "train/1229.png"}
{"question": "Use parallelogram ABCD to find $m\\angle BDC$", "answer": "87.9", "image_path": "train/1230.png"}
{"question": "Find $x$.", "answer": "40", "image_path": "train/1231.png"}
{"question": "The lengths of the bases of an isosceles trapezoid are shown below. If the perimeter is 74 meters, what is its area?", "answer": "162", "image_path": "train/1232.png"}
{"question": "Find $m \\widehat {RQ}$.", "answer": "28", "image_path": "train/1233.png"}
{"question": "Find $FE$ if $AB=6, AF=8, BC=x, CD=y$, $DE=2y-3,$ and $FE=x+\\frac{10}{3}$.", "answer": "\\frac { 40 } { 3 }", "image_path": "train/1234.png"}
{"question": "Find the perimeter of the figure. Round to the nearest tenth if necessary.", "answer": "56", "image_path": "train/1235.png"}
{"question": "What is the measure of an interior angle of a regular pentagon?", "answer": "108", "image_path": "train/1236.png"}
{"question": "Find the measure of $\\angle 4$ if $\\overline{AB} \\perp \\overline{BC}$.", "answer": "40", "image_path": "train/1237.png"}
{"question": "Find x.", "answer": "\\frac { \\sqrt { 10 } } { 5 }", "image_path": "train/1238.png"}
{"question": "Find x. Round to the nearest tenth.", "answer": "28.7", "image_path": "train/1239.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth.", "answer": "34.6", "image_path": "train/1240.png"}
{"question": "In the figure, $m∠3 = 43$. Find the measure of $\\angle 2$.", "answer": "137", "image_path": "train/1241.png"}
{"question": "Find x in the figure below. Round your answer to the nearest tenth if necessary.", "answer": "93.9", "image_path": "train/1242.png"}
{"question": "Find $m \\angle R$.", "answer": "30", "image_path": "train/1243.png"}
{"question": "Find $x$ so that each quadrilateral is a parallelogram.", "answer": "7", "image_path": "train/1244.png"}
{"question": "If $a ∥ b$ in the diagram below, which of the following may not be true?", "answer": "\\angle 8 \\cong \\angle 2", "image_path": "train/1245.png"}
{"question": "Find x in the parallelogram", "answer": "7", "image_path": "train/1246.png"}
{"question": "Find the area of the triangle. Round to the nearest tenth if necessary.", "answer": "129.9", "image_path": "train/1247.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "9.6", "image_path": "train/1248.png"}
{"question": "Express the ratio of $\\sin Q$ as a decimal to the nearest hundredth.", "answer": "0.47", "image_path": "train/1249.png"}
{"question": "parallelogram MNPQ with $m \\angle M=10 x$ and $m \\angle N=20 x$, find $\\angle N$", "answer": "120", "image_path": "train/1250.png"}
{"question": "Find the measure of the altitude drawn to the hypotenuse.", "answer": "8 \\sqrt { 2 }", "image_path": "train/1251.png"}
{"question": "In the figure at the right, $YZ$ is the midsegment of trapezoid $TWRV$. Determine the value of $x$.", "answer": "1.2", "image_path": "train/1252.png"}
{"question": "Find $x$.", "answer": "162", "image_path": "train/1253.png"}
{"question": "Find $\\angle 10$", "answer": "50", "image_path": "train/1254.png"}
{"question": "Find $x$.", "answer": "6", "image_path": "train/1255.png"}
{"question": "$m∠11 = 4x$, $m∠12 = 2x -6 $. Find the measure of $\\angle 11$.", "answer": "124", "image_path": "train/1256.png"}
{"question": "Find $m \\angle 3$.", "answer": "16", "image_path": "train/1257.png"}
{"question": "Find $x$ so that $ m \\parallel n $.", "answer": "21.6", "image_path": "train/1258.png"}
{"question": "Find $m\\angle E$", "answer": "126", "image_path": "train/1259.png"}
{"question": "Find the base of the parallelogram given its area with 100 square units.", "answer": "20", "image_path": "train/1260.png"}
{"question": "If $\\overline{P Q} \\cong \\overline{Q S}$, $\\overline{Q R} \\cong \\overline{R S}$, and $m \\angle P R S=72$, what is the measure of $\\angle Q P S$ ?", "answer": "27", "image_path": "train/1261.png"}
{"question": "In $\\odot O, \\overline{E C}$ and $\\overline{A B}$ are diameters, and $\\angle B O D \\cong \\angle D O E \\cong \\angle E O F \\cong \\angle F O A$\r\nFind $m\\widehat{A D C}$", "answer": "270", "image_path": "train/1262.png"}
{"question": "Quadrilateral ABCD is a rectangle. If $m\\angle ADB = 4x + 8$ and $m\\angle DBA = 6x + 12$, find x.", "answer": "7", "image_path": "train/1263.png"}
{"question": "Express the ratio of $\\sin B$ as a decimal to the nearest hundredth.", "answer": "0.92", "image_path": "train/1264.png"}
{"question": "Find $m∠MRQ$ so that $a || b$.", "answer": "77", "image_path": "train/1265.png"}
{"question": "$m∠19 = 100 + 20x$, $m∠20 = 20x $. Find the measure of $\\angle 20$.", "answer": "40", "image_path": "train/1266.png"}
{"question": "Find $x$.", "answer": "4", "image_path": "train/1267.png"}
{"question": "Find the perimeter of $\\triangle Q R S$ if $\\triangle Q R S \\sim \\triangle Q T P$", "answer": "14", "image_path": "train/1268.png"}
{"question": "Find $y$.", "answer": "40", "image_path": "train/1269.png"}
{"question": "Polygon ABCD ~ polygon AEFG, $m\\angle AGF = 108$, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26.\r\nFind DC", "answer": "22.4", "image_path": "train/1270.png"}
{"question": "Find z.", "answer": "\\frac { 85 } { 6 } \\sqrt { 13 }", "image_path": "train/1271.png"}
{"question": "Rhombus $QRST$ has an area of 137.9 square meters. If $RT$ is 12.2 meters, find $QS$.", "answer": "22.6", "image_path": "train/1272.png"}
{"question": "Find $y$.", "answer": "8", "image_path": "train/1273.png"}
{"question": "Find the area of a regular pentagon with a perimeter of 40 centimeters.", "answer": "110", "image_path": "train/1274.png"}
{"question": "Find x.", "answer": "2 \\sqrt { 66 }", "image_path": "train/1275.png"}
{"question": "Square $F G H J$ is inscribed in $\\odot K$. Find the measure of a central angle.", "answer": "90", "image_path": "train/1276.png"}
{"question": "Find the exact circumference of each circle.", "answer": "8 \\pi", "image_path": "train/1277.png"}
{"question": "Find $x$.", "answer": "140", "image_path": "train/1278.png"}
{"question": "Find the measure of $\\angle 3$ if $m \\angle D G F=53$ and $m \\angle A G C=40$.", "answer": "50", "image_path": "train/1279.png"}
{"question": "Polygon $BCDE$ $\\cong$ polygon $RSTU$. Find $x$.", "answer": "20", "image_path": "train/1280.png"}
{"question": "$\\triangle NDG \\cong \\triangle LGD$. Find $x$.", "answer": "54", "image_path": "train/1281.png"}
{"question": "WXYZ is a kite. If $m\\angle WXY = 120$, $m\\angle WZY = 4x$, and $m\\angle ZWX = 10x$, find $m\\angle ZYX$.", "answer": "100", "image_path": "train/1282.png"}
{"question": "$P$ is the centroid of triangle $QUS$. If $QP=14$ centimeters, what is the length of $\\overline{QT}$?", "answer": "21", "image_path": "train/1283.png"}
{"question": "Express the ratio of $\\cos Q$ as a decimal to the nearest hundredth.", "answer": "0.88", "image_path": "train/1284.png"}
{"question": "$\\overline{JH}$ is a midsegment of $\\triangle KLM$. Find $x$.", "answer": "10", "image_path": "train/1285.png"}
{"question": "For isosceles trapezoid $A B C D$, $X$ and $Y$ are midpoints of the legs. Find $m \\angle X B C$ if $m \\angle A D Y=78$", "answer": "102", "image_path": "train/1286.png"}
{"question": "If $FK = 3x - 1$, $KG = 4y + 3$, $JK = 6y - 2$, and \r\n$KH = 2x + 3$, find $y$ so that the quadrilateral is a parallelogram. ", "answer": "2.5", "image_path": "train/1287.png"}
{"question": "Find $x$.", "answer": "12", "image_path": "train/1288.png"}
{"question": "Find x.", "answer": "9 \\sqrt { 2 }", "image_path": "train/1289.png"}
{"question": "Find $m \\angle 1$ in the figure.", "answer": "107", "image_path": "train/1290.png"}
{"question": "Find $a$.", "answer": "15", "image_path": "train/1291.png"}
{"question": "Find the measure of $\\angle 8$ if $\\overline{A B} \\perp \\overline{B C}$.", "answer": "14", "image_path": "train/1292.png"}
{"question": "Find the area of the shaded region. Assume the inscribed polygon is regular.", "answer": "25.8", "image_path": "train/1293.png"}
{"question": "Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.", "answer": "54.4", "image_path": "train/1294.png"}
{"question": "If $c=8,$ find $a$", "answer": "4", "image_path": "train/1295.png"}
{"question": "If $MNPQ \\sim XYZW,$ find the perimeter of $MNPQ$.", "answer": "34", "image_path": "train/1296.png"}
{"question": "Find $x$.", "answer": "20", "image_path": "train/1297.png"}
{"question": "In $\\odot P, m \\widehat{E N}=66$ and $m \\angle G P M=89$ . \r\nFind $m \\angle E G N$", "answer": "33", "image_path": "train/1298.png"}
{"question": "In the figure, $m∠1 = 123$. Find the measure of $\\angle 5$.", "answer": "123", "image_path": "train/1299.png"}
{"question": "Find $SR$.", "answer": "4", "image_path": "train/1300.png"}
{"question": "If TP = 4x + 2, QP = 2y – 6, PS = 5y - 12, and PR = 6x - 4, find x so that the quadrilateral is a parallelogram.", "answer": "3", "image_path": "train/1301.png"}
{"question": "$\\triangle K L N$ and $\\triangle L M N$ are isosceles and $m \\angle J K N=130$. Find the measure of $\\angle M$.", "answer": "140", "image_path": "train/1302.png"}
{"question": "Find $x$ so that the quadrilateral is a parallelogram.", "answer": "8", "image_path": "train/1303.png"}
{"question": "Find $m\\angle D$", "answer": "60", "image_path": "train/1304.png"}
{"question": "$\\odot  C \\cong \\odot D$, Find $x$.", "answer": "27", "image_path": "train/1305.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram", "answer": "15.5", "image_path": "train/1306.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "12.8", "image_path": "train/1307.png"}
{"question": "In $\\odot R, S U=20, Y W=20,$ and $m \\widehat{Y X}=45$.\r\nFind UV", "answer": "10", "image_path": "train/1308.png"}
{"question": "Find $m \\widehat {RQS}$ if $m \\widehat{QTS}=238$.", "answer": "61", "image_path": "train/1309.png"}
{"question": "Find the measure of the altitude drawn to the hypotenuse.", "answer": "3 \\sqrt { 5 }", "image_path": "train/1310.png"}
{"question": "If $b=3,$ find $c$", "answer": "2 \\sqrt { 3 }", "image_path": "train/1311.png"}
{"question": "If $m \\angle 2=70-4 x$ and $m \\angle 5=18 x-8,$ find $m \\angle 5$", "answer": "28", "image_path": "train/1312.png"}
{"question": "Find $y$.", "answer": "4", "image_path": "train/1313.png"}
{"question": "Find $m \\angle 4$.", "answer": "95", "image_path": "train/1314.png"}
{"question": "Find $EG$.", "answer": "10", "image_path": "train/1315.png"}
{"question": "Find $x$.", "answer": "9", "image_path": "train/1316.png"}
{"question": "Find the scale factor from $W$ to $W'$.", "answer": "0.6", "image_path": "train/1317.png"}
{"question": "Find x.", "answer": "18", "image_path": "train/1318.png"}
{"question": "If $\\angle R S T$ is a right angle, $\\overline{SU} \\perp \\overline{RT}$, $\\overline{UV} \\perp \\overline{ST},$ and $m \\angle RT S=47,$ find $m \\angle TUV$", "answer": "43", "image_path": "train/1319.png"}
{"question": "Find y. Round to the nearest tenth, if necessary.", "answer": "8.6", "image_path": "train/1320.png"}
{"question": "Find $x$.", "answer": "8", "image_path": "train/1321.png"}
{"question": "ABCD is a rhombus. If EB = 9, AB = 12 and $m\\angle ABD = 55$ . Find AE", "answer": "\\sqrt { 63 }", "image_path": "train/1322.png"}
{"question": "Quadrilateral ABCD is a rectangle. $m\\angle 2 = 40$. Find $m \\angle 6$", "answer": "50", "image_path": "train/1323.png"}
{"question": "If PR || KL, KN = 9, LN = 16, PM = 2 KP, find KP", "answer": "5", "image_path": "train/1324.png"}
{"question": "Find $m \\angle ABD$.", "answer": "103", "image_path": "train/1325.png"}
{"question": "Find x", "answer": "5.5", "image_path": "train/1326.png"}
{"question": "If $\\overline{MS}$ is a median of $ \\triangle MNQ$, $QS = 3a - 14$, $SN = 2a + 1$, and $m∠MSQ = 7a + 1$, find the value of $a$.", "answer": "15", "image_path": "train/1327.png"}
{"question": "If QRST is a parallelogram, find $y$", "answer": "9", "image_path": "train/1328.png"}
{"question": "Find the measure of $\\angle D$", "answer": "46", "image_path": "train/1329.png"}
{"question": "Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.", "answer": "10.6", "image_path": "train/1330.png"}
{"question": "In $\\odot G, m \\angle A G B=30$ and $\\overline{C G} \\perp \\overline{G D}$.\r\nFind $m \\widehat{C D F}$", "answer": "120", "image_path": "train/1331.png"}
{"question": "If $CE=t-2$. $EB=t+1$, $CD=2$, and $CA=10$, find $t$.", "answer": "3", "image_path": "train/1332.png"}
{"question": "Find z.", "answer": "\\frac { \\sqrt { 2 } } { 3 }", "image_path": "train/1333.png"}
{"question": "Use the Pythagorean Theorem to find the length of the hypotenuse of each right triangle.", "answer": "5", "image_path": "train/1334.png"}
{"question": "Use rhombus $A B C D$ with $m \\angle 1=2 x+20, m \\angle 2=5 x-4$, $A C=15,$ and $m \\angle 3=y^{2}+26 .$ \r\nFind AF", "answer": "7.5", "image_path": "train/1335.png"}
{"question": "Find the area of the shaded region formed by the circle and regular polygon. Round to the nearest tenth.", "answer": "1.9", "image_path": "train/1336.png"}
{"question": "In $\\odot O, \\overline{E C}$ and $\\overline{A B}$ are diameters, and $\\angle B O D \\cong \\angle D O E \\cong \\angle E O F \\cong \\angle F O A$\r\nFind $m\\widehat{E B}$", "answer": "90", "image_path": "train/1337.png"}
{"question": "Find the measure of $∠Z$ to the nearest tenth.", "answer": "36.9", "image_path": "train/1338.png"}
{"question": "Find the area of the regular polygon. Round to the nearest tenth.", "answer": "59.4", "image_path": "train/1339.png"}
{"question": "Find x", "answer": "2", "image_path": "train/1340.png"}
{"question": "Find $m \\angle A$.", "answer": "85", "image_path": "train/1341.png"}
{"question": "Find y", "answer": "9.6 \\sqrt { 2 }", "image_path": "train/1342.png"}
{"question": "Find $m \\angle C$.", "answer": "49", "image_path": "train/1343.png"}
{"question": "Use rectangle LMNP, parallelogram LKMJ to solve the problem.\r\nIf $m \\angle M J N=35,$ find $m \\angle M P N$", "answer": "17.5", "image_path": "train/1344.png"}
{"question": "The segment is tangent to the circle. Find $x$.", "answer": "9", "image_path": "train/1345.png"}
{"question": "$H$ is the incenter of $\\triangle ABC$. Find $m \\angle DHG$.", "answer": "120", "image_path": "train/1346.png"}
{"question": "What is the measure of $\\angle KLM$.", "answer": "32", "image_path": "train/1347.png"}
{"question": "Trapezoid $NOPQ$ has an area of 250 square inches. Find the height of $NOPQ$.", "answer": "10", "image_path": "train/1348.png"}
{"question": "Find $y$ so that each quadrilateral is a parallelogram.", "answer": "16", "image_path": "train/1349.png"}
{"question": "$m \\widehat{J H}=114$ Find $m\\angle 2$", "answer": "57", "image_path": "train/1350.png"}
{"question": "Find the measure of $RS$ of equilateral triangle $RST$ if $RS = x + 9$, $ST = 2x$, and $RT = 3x - 9$.", "answer": "18", "image_path": "train/1351.png"}
{"question": "Find $x$ and so that each quadrilateral is a parallelogram.", "answer": "8", "image_path": "train/1352.png"}
{"question": "Use parallelogram MNPR to find $m \\angle MQR$", "answer": "83", "image_path": "train/1353.png"}
{"question": "Find x.", "answer": "5", "image_path": "train/1354.png"}
{"question": "Find x.", "answer": "6", "image_path": "train/1355.png"}
{"question": "Find $MN$ if $\\triangle JMN$ is an isosceles triangle with $\\overline{JM} \\cong \\overline{M N}$.", "answer": "3", "image_path": "train/1356.png"}
{"question": "Find x.", "answer": "14", "image_path": "train/1357.png"}
{"question": "$\\overline{QS}$ is a diameter of $\\odot V$. Find $m \\widehat {PQR}$.", "answer": "123", "image_path": "train/1358.png"}
{"question": "Find AB", "answer": "10", "image_path": "train/1359.png"}
{"question": "Find $x$ so that $ m \\parallel n $.", "answer": "- 8", "image_path": "train/1360.png"}
{"question": "In the figure, $m ∠1 = 53$. Find the measure of $∠2$.", "answer": "127", "image_path": "train/1361.png"}
{"question": "Find $y$ so that each quadrilateral is a parallelogram.", "answer": "44", "image_path": "train/1362.png"}
{"question": "Quadrilateral ABCD is a rectangle. $m\\angle 2 = 40$. Find $m \\angle 1$", "answer": "50", "image_path": "train/1363.png"}
{"question": "Find $x$.", "answer": "150", "image_path": "train/1364.png"}
{"question": "Find x.", "answer": "8.4", "image_path": "train/1365.png"}
{"question": "Find y", "answer": "\\sqrt { 33 }", "image_path": "train/1366.png"}
{"question": "Find $m\\angle M$", "answer": "96", "image_path": "train/1367.png"}
{"question": "In $\\odot X, A B=30, C D=30,$ and $m \\widehat{C Z}=40$\r\nFind $m\\widehat{Y B}$", "answer": "40", "image_path": "train/1368.png"}
{"question": "Find $m \\angle 3$.", "answer": "29", "image_path": "train/1369.png"}
{"question": "Find $m \\widehat {VX}$.", "answer": "152", "image_path": "train/1370.png"}
{"question": "What is the value of x in the figure?", "answer": "12", "image_path": "train/1371.png"}
{"question": "Find x. Assume that any segment that appears to be tangent is tangent.", "answer": "130", "image_path": "train/1372.png"}
{"question": "In A, the radius is $14$ and $CD = 22$. Find $CE$.", "answer": "11", "image_path": "train/1373.png"}
{"question": "Find the area of the shaded region.", "answer": "47.7", "image_path": "train/1374.png"}
{"question": "Find y", "answer": "8 \\sqrt { 3 }", "image_path": "train/1375.png"}
{"question": "Find the area of the regular polygon figure. Round to the nearest tenth.", "answer": "166.3", "image_path": "train/1376.png"}
{"question": "Find the measure of $\\angle 2$.", "answer": "25", "image_path": "train/1377.png"}
{"question": "In the figure, $m ∠9 = 75$. Find the measure of $\\angle 5$.", "answer": "75", "image_path": "train/1378.png"}
{"question": "Find the area of the figure. Round to the nearest tenth.", "answer": "105.7", "image_path": "train/1379.png"}
{"question": "In the figure, $ \\triangle ABC$ is isosceles, $ \\triangle DCE$ is equilateral, and $ \\triangle FCG$ is isosceles. Find the measure of the $\\angle 2$ at vertex $C$.", "answer": "17", "image_path": "train/1380.png"}
{"question": "Find x", "answer": "37", "image_path": "train/1381.png"}
{"question": "If $m \\angle 1=3 x+40$, $m \\angle 2=2(y-10)$, and $m \\angle 3=2 x+70$, find $x$.", "answer": "30", "image_path": "train/1382.png"}
{"question": "$Q$ is the centroid and $BE=9$. Find $QE$.", "answer": "3", "image_path": "train/1383.png"}
{"question": "Find the perimeter of the $\\triangle DEF$, if $\\triangle ABC \\sim \\triangle DEF$, $AB=5, BC=6, AC=7$, and $DE=3$.", "answer": "10.8", "image_path": "train/1384.png"}
{"question": "In $\\odot R, S U=20, Y W=20,$ and $m \\widehat{Y X}=45$.\r\nFind $m\\widehat{S T}$", "answer": "45", "image_path": "train/1385.png"}
{"question": "Suppose $B D=12$ millimeters. Find the radius of the circle.", "answer": "6", "image_path": "train/1386.png"}
{"question": "Find the rhombus of the kite.", "answer": "240", "image_path": "train/1387.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth.", "answer": "4.5", "image_path": "train/1388.png"}
{"question": "In the figure, $a ∥ b, c ∥ d$, and $m∠4 = 57$. Find the measure of $\\angle 10$.", "answer": "57", "image_path": "train/1389.png"}
{"question": "Find $x$.", "answer": "3", "image_path": "train/1390.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "28", "image_path": "train/1391.png"}
{"question": "Find $y$.", "answer": "6", "image_path": "train/1392.png"}
{"question": "Find x.", "answer": "21", "image_path": "train/1393.png"}
{"question": "Find $m \\widehat{B X}$", "answer": "117", "image_path": "train/1394.png"}
{"question": "Find $m \\angle 3$.", "answer": "133", "image_path": "train/1395.png"}
{"question": "What is the value of tan x?", "answer": "\\frac { 5 } { 12 }", "image_path": "train/1396.png"}
{"question": "If TP = 4x + 2, QP = 2y – 6, PS = 5y - 12, and PR = 6x - 4, find y so that the quadrilateral is a parallelogram.", "answer": "2", "image_path": "train/1397.png"}
{"question": "Find $b$ in the given parallelogram", "answer": "8", "image_path": "train/1398.png"}
{"question": "Each pair of polygons is similar. Find y", "answer": "14", "image_path": "train/1399.png"}
{"question": "Find the exact circumference of each circle.", "answer": "10 \\pi \\sqrt { 2 }", "image_path": "train/1400.png"}
{"question": "$P$ is the incenter of $\\angle XYZ$. Find $PK$.", "answer": "16", "image_path": "train/1401.png"}
{"question": "Find $XZ$.", "answer": "23", "image_path": "train/1402.png"}
{"question": "In the figure, $m∠2= 110$ and $m ∠ 12 = 55$. Find the measure of $∠2$.", "answer": "70", "image_path": "train/1403.png"}
{"question": "Use parallelogram ABCD to find CD", "answer": "6", "image_path": "train/1404.png"}
{"question": "Find $m \\angle K$.", "answer": "46", "image_path": "train/1405.png"}
{"question": "Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.", "answer": "271.2", "image_path": "train/1406.png"}
{"question": "Find x", "answer": "20", "image_path": "train/1407.png"}
{"question": "Find x.", "answer": "2 \\sqrt { 78 }", "image_path": "train/1408.png"}
{"question": "Find $y$ so that each quadrilateral is a parallelogram.", "answer": "4", "image_path": "train/1409.png"}
{"question": "$\\overline{AD}$ and $\\overline{CG}$ are diameters of $\\odot B$. Find $m \\widehat {CD}$.", "answer": "55", "image_path": "train/1410.png"}
{"question": "Find the measure of $\\angle C$", "answer": "110", "image_path": "train/1411.png"}
{"question": "Find $m\\angle Q$", "answer": "60", "image_path": "train/1412.png"}
{"question": "Find $JN$ if $\\triangle JMN$ is an isosceles triangle with $\\overline{JM} \\cong \\overline{M N}$.", "answer": "2", "image_path": "train/1413.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent. ", "answer": "\\sqrt { 193 }", "image_path": "train/1414.png"}
{"question": "Find the area of the regular polygon. Round to the nearest tenth.", "answer": "98", "image_path": "train/1415.png"}
{"question": "Find the perimeter of the figure in feet. Round to the nearest tenth, if necessary.", "answer": "16", "image_path": "train/1416.png"}
{"question": "Find the area of the blue sector.", "answer": "4.6 \\pi", "image_path": "train/1417.png"}
{"question": "What is ED?", "answer": "not enough information", "image_path": "train/1418.png"}
{"question": "What is the area of rectangle $WXYZ$?", "answer": "18.6", "image_path": "train/1419.png"}
{"question": "$\\triangle FGH$ is an equilateral triangle. Find $HG$.", "answer": "19", "image_path": "train/1420.png"}
{"question": "$H$ is the incenter of $\\triangle ABC$. Find $m \\angle HAC$.", "answer": "32", "image_path": "train/1421.png"}
{"question": "Find $m \\angle JKL$.", "answer": "60", "image_path": "train/1422.png"}
{"question": "Find x", "answer": "\\frac { 3 } { 7 }", "image_path": "train/1423.png"}
{"question": "For the pair of similar figures, find the area of the green figure.", "answer": "672", "image_path": "train/1424.png"}
{"question": "If $\\overline{AB}$ and $\\overline{JK}$ are altitudes, $\\triangle DAC \\sim \\triangle MJL, AB=9, AD=4x-8, JK=21$, and $JM=5x+3,$ find $x$.", "answer": "5", "image_path": "train/1425.png"}
{"question": "For the pair of similar figures, find the area of the green figure.", "answer": "240", "image_path": "train/1426.png"}
{"question": "Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.", "answer": "18.5", "image_path": "train/1427.png"}
{"question": "Find x. Round the angle measure to the nearest degree.", "answer": "15", "image_path": "train/1428.png"}
{"question": "find $cosR$", "answer": "0.6", "image_path": "train/1429.png"}
{"question": "Find x", "answer": "8.5", "image_path": "train/1430.png"}
{"question": "Find x", "answer": "59", "image_path": "train/1431.png"}
{"question": "Find the length of $\\widehat {AB}$. Round to the nearest hundredth.", "answer": "2.36", "image_path": "train/1432.png"}
{"question": "Find the area of the figure.", "answer": "112.5", "image_path": "train/1433.png"}
{"question": "Quadrilateral ABCD is a rectangle. $m\\angle 2 = 40$. Find $m \\angle 5$", "answer": "80", "image_path": "train/1434.png"}
{"question": "Find y.", "answer": "6", "image_path": "train/1435.png"}
{"question": "For trapezoid QRTU, V and S are midpoints of the legs. If TU = 26 and SV = 17, find QR.", "answer": "8", "image_path": "train/1436.png"}
{"question": "Find the measure of $\\angle 1$ if $m∠4= m∠5$.", "answer": "64", "image_path": "train/1437.png"}
{"question": "Find $m \\angle 3$.", "answer": "26", "image_path": "train/1438.png"}
{"question": "In $\\odot F$, find $m \\widehat {ADB}$.", "answer": "243", "image_path": "train/1439.png"}
{"question": "In $\\odot P$, $RT=11$, find $m \\widehat {QRS}$. Round to the nearest hundredth.", "answer": "19.01", "image_path": "train/1440.png"}
{"question": "Triangle $JKL$ is circumscribed about $\\odot R$. Find the perimeter of $\\triangle JKL$.", "answer": "52", "image_path": "train/1441.png"}
{"question": "Find x.", "answer": "6 \\sqrt { 3 }", "image_path": "train/1442.png"}
{"question": "$\\overline{HK}$ and $\\overline{IG}$ are diameters of $\\odot L$. Find $m \\widehat {HI}$.", "answer": "59", "image_path": "train/1443.png"}
{"question": "In the figure, the vertices of quadrilateral ABCD intersect square EFGH and divide its sides into segments with measures that have a ratio of 1:2. Find the ratio between the areas of ABCD and EFGH.", "answer": "5:9", "image_path": "train/1444.png"}
{"question": "find $tanR$", "answer": "\\frac { 4 } { 3 }", "image_path": "train/1445.png"}
{"question": "Find x.", "answer": "24", "image_path": "train/1446.png"}
{"question": "Find $m \\widehat{CD}$.", "answer": "150", "image_path": "train/1447.png"}
{"question": "In the figure, $ m ∠1 = 3a + 40 $, $ m ∠2 = 2a + 25 $, and $ m ∠3 = 5b - 26 $. Find $a$.", "answer": "23", "image_path": "train/1448.png"}
{"question": "For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure. ", "answer": "\\frac { 4 } { 5 }", "image_path": "train/1449.png"}
{"question": "The diameters of $\\odot A, \\odot B,$ and $\\odot C$ are 10, 30 and 10 units, respectively. Find BX if $\\overline{A Z} \\cong \\overline{C W}$ and $C W=2$.", "answer": "12", "image_path": "train/1450.png"}
{"question": "If $TU=14$, what it the radius of $\\odot Q$.", "answer": "7", "image_path": "train/1451.png"}
{"question": "Find $x$. Round to the nearest tenth.", "answer": "20.1", "image_path": "train/1452.png"}
{"question": "Find x. Round side measures to the nearest tenth.", "answer": "30.0", "image_path": "train/1453.png"}
{"question": "Find the area of the figure.", "answer": "56", "image_path": "train/1454.png"}
{"question": "Find $\\angle 2$", "answer": "47", "image_path": "train/1455.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "36", "image_path": "train/1456.png"}
{"question": "Solve for x in parallelogram RSTU.", "answer": "30", "image_path": "train/1457.png"}
{"question": "$\\overline{BC} \\| \\overline{DF}$. $AB=x+5$, $BD=12$, $AC=3x+1$, and $CF=15$. Find $x$.", "answer": "3", "image_path": "train/1458.png"}
{"question": "Find $m \\angle JKL$.", "answer": "31", "image_path": "train/1459.png"}
{"question": "Find the measure of $\\angle C$. Round to the nearest degree.", "answer": "56", "image_path": "train/1460.png"}
{"question": "Find AB", "answer": "60", "image_path": "train/1461.png"}
{"question": "Find the perimeter of the given triangle $\\triangle D E F,$ if $\\triangle A B C \\sim \\triangle D E F, A B=5$, $B C=6, A C=7,$ and $D E=3$", "answer": "10.8", "image_path": "train/1462.png"}
{"question": "Find x.", "answer": "10", "image_path": "train/1463.png"}
{"question": "Find x.", "answer": "5 \\sqrt { 2 }", "image_path": "train/1464.png"}
{"question": "Find $JM$ if $\\triangle JMN$ is an isosceles triangle with $\\overline{JM} \\cong \\overline{M N}$.", "answer": "3", "image_path": "train/1465.png"}
{"question": "In rectangle JKLM shown below, $\\overline{J L}$ and $M K$ are diagonals. If $J L=2 x+5$ and $K M=4 x-11$, what is $ x $ ? ", "answer": "8", "image_path": "train/1466.png"}
{"question": "Find the measure of $\\angle DFB$ on $\\odot F$ with diameter $\\overline{AC} $.", "answer": "165", "image_path": "train/1467.png"}
{"question": "Find x. Round to the nearest tenth.", "answer": "23.2", "image_path": "train/1468.png"}
{"question": "Find $JL$.", "answer": "12", "image_path": "train/1469.png"}
{"question": "Find $RT$.", "answer": "10", "image_path": "train/1470.png"}
{"question": "If $a=10 \\sqrt{3},$ find $y$ ", "answer": "15 \\sqrt { 3 }", "image_path": "train/1471.png"}
{"question": "If $LK=4,MP=3,PQ=6,KJ=2,RS=6$, and $LP=2$, find $QK$.", "answer": "6", "image_path": "train/1472.png"}
{"question": "The square is circumscribed to the circle. Find the exact circumference of the circle.", "answer": "25 \\pi", "image_path": "train/1473.png"}
{"question": "QRST is an isosceles trapezoid with median $\\overline{X Y}$\r\nFind $T S$ if $Q R=22$ and $X Y=15$", "answer": "8", "image_path": "train/1474.png"}
{"question": "Find the area of the triangle. Round to the nearest tenth if necessary.", "answer": "240", "image_path": "train/1475.png"}
{"question": "Find $DF$.", "answer": "5", "image_path": "train/1476.png"}
{"question": "Find $x$.", "answer": "18", "image_path": "train/1477.png"}
{"question": "Find $x$.", "answer": "11", "image_path": "train/1478.png"}
{"question": "Use parallelogram $ABCD$ to find $AB$", "answer": "12", "image_path": "train/1479.png"}
{"question": "Find the perimeter of the figure in feet. Round to the nearest tenth, if necessary.", "answer": "28", "image_path": "train/1480.png"}
{"question": "In the figure, $m∠4 = 101$. Find the measure of $\\angle 5$.", "answer": "79", "image_path": "train/1481.png"}
{"question": "Find $x$.", "answer": "4", "image_path": "train/1482.png"}
{"question": "Find x.", "answer": "\\frac { 39 \\sqrt { 2 } } { 2 }", "image_path": "train/1483.png"}
{"question": "Find $m \\angle PNM$.", "answer": "88", "image_path": "train/1484.png"}
{"question": "$\\triangle JKL \\sim \\triangle WYZ$. Find $y$.", "answer": "65", "image_path": "train/1485.png"}
{"question": "Express the ratio of $\\sin L$ as a decimal to the nearest hundredth.", "answer": "0.38", "image_path": "train/1486.png"}
{"question": "Find $x$.", "answer": "2", "image_path": "train/1487.png"}
{"question": "If $x=7 \\sqrt{3},$ find $b$", "answer": "42", "image_path": "train/1488.png"}
{"question": "If $P T=y-3, P S=y+2, R S=12,$ and $Q S=16$\r\nsolve for $y$", "answer": "\\frac { 14 } { 3 }", "image_path": "train/1489.png"}
{"question": "Find $z$.", "answer": "14", "image_path": "train/1490.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "16", "image_path": "train/1491.png"}
{"question": "For the pair of similar figures, use the given areas to find $x$.", "answer": "4.3", "image_path": "train/1492.png"}
{"question": "Use a Pythagorean Triple to find x.", "answer": "30", "image_path": "train/1493.png"}
{"question": "Each pair of polygons is similar. Find EG", "answer": "15.525", "image_path": "train/1494.png"}
{"question": "Use parallelogram to  find $x$", "answer": "5", "image_path": "train/1495.png"}
{"question": "If $m \\angle AED=95$ and $m \\widehat{AD}=120$, what is $m \\angle BAC$?", "answer": "35", "image_path": "train/1496.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "471.9", "image_path": "train/1497.png"}
{"question": "In $\\triangle RST$, $Z$ is the centroid and $RZ=18$. Find $SR$.", "answer": "28", "image_path": "train/1498.png"}
{"question": "If $ABCDE \\sim PQRST,$ find the perimeter of $ABCDE$.", "answer": "30", "image_path": "train/1499.png"}
{"question": "Find x. Round to the nearest tenth, if necessary.", "answer": "11", "image_path": "train/1500.png"}
{"question": "Find $x$ so that each quadrilateral is a parallelogram.", "answer": "1", "image_path": "train/1501.png"}
{"question": "Find x", "answer": "2 \\sqrt { 6 }", "image_path": "train/1502.png"}
{"question": "Find $x$.", "answer": "7", "image_path": "train/1503.png"}
{"question": "Find the value of the variable $x$ in the figure.", "answer": "114", "image_path": "train/1504.png"}
{"question": "Find x. Round to the nearest tenth.", "answer": "9.2", "image_path": "train/1505.png"}
{"question": "Find the value of $x$.", "answer": "35", "image_path": "train/1506.png"}
{"question": "Find $y$ so that each quadrilateral is a parallelogram.", "answer": "4", "image_path": "train/1507.png"}
{"question": "Find $z$ in the figure.", "answer": "13.5", "image_path": "train/1508.png"}
{"question": "In the figure, $m \\angle 1=4 p+15$, $m \\angle 3=3 p-10$ and $m \\angle 4=6 r+5 $. Find the value of $r$.", "answer": "10", "image_path": "train/1509.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "855", "image_path": "train/1510.png"}
{"question": "Find x.", "answer": "52", "image_path": "train/1511.png"}
{"question": "Find $y$.", "answer": "15.6", "image_path": "train/1512.png"}
{"question": "Find x. Assume that any segment that appears to be tangent is tangent.", "answer": "5", "image_path": "train/1513.png"}
{"question": "In the figure, $a ∥ b, c ∥ d$, and $m∠4 = 57$. Find the measure of $\\angle 5$.", "answer": "123", "image_path": "train/1514.png"}
{"question": "Find the area of the figure. Round to the nearest tenth.", "answer": "87.5", "image_path": "train/1515.png"}
{"question": "Find x.", "answer": "6 \\sqrt 2", "image_path": "train/1516.png"}
{"question": "In the figure at the right, which cannot be true if $ m \\parallel l $ and $ m ∠1 = 73 $?", "answer": "\\angle 1 \\cong \\angle 4", "image_path": "train/1517.png"}
{"question": "Find the perimeter of each polygon for the given information.\r\n$C F=6(3-x), D B=12 y-4$", "answer": "36", "image_path": "train/1518.png"}
{"question": "Find $x$.", "answer": "75", "image_path": "train/1519.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram.", "answer": "7", "image_path": "train/1520.png"}
{"question": "Solve for x in the figure below.", "answer": "4.75", "image_path": "train/1521.png"}
{"question": "Find x. Round to the nearest tenth.", "answer": "7.2", "image_path": "train/1522.png"}
{"question": "Find x", "answer": "3", "image_path": "train/1523.png"}
{"question": "Find the area of the shaded region. Assume that the polygon is regular unless otherwise stated. Round to the nearest tenth.", "answer": "154.2", "image_path": "train/1524.png"}
{"question": "Find $a$ if $c=8, b=10,$ and $m \\angle A=60$", "answer": "9.2", "image_path": "train/1525.png"}
{"question": "In $\\odot C$, $m \\angle HCG=2x$ and $m \\angle HCD=6x+28$, find $m \\widehat {EF}$.", "answer": "52", "image_path": "train/1526.png"}
{"question": "In $\\odot F, \\overline{F H} \\cong \\overline{F L}$ and $\\mathrm{FK}=17$.\r\nFind KM", "answer": "30", "image_path": "train/1527.png"}
{"question": "In $\\odot F, m \\angle D F A=50$ and $\\overline{C F} \\perp \\overline{F B}$. Find $m \\widehat{C B E}$", "answer": "140", "image_path": "train/1528.png"}
{"question": "In the figure, $m∠3 = 110$ and $m ∠ 12 = 55$. Find the measure of $∠10$.", "answer": "55", "image_path": "train/1529.png"}
{"question": "If $\\overline{W P}$ is a perpendicular bisector, $m \\angle WHA=8 q+17$, $m \\angle HWP=10+q$, $AP=6 r+4$, and $PH=22+3 r$, find $m \\angle HWP$.", "answer": "17", "image_path": "train/1530.png"}
{"question": "Find x", "answer": "91", "image_path": "train/1531.png"}
{"question": "Find x. Round to the nearest tenth.\r\n", "answer": "9.9", "image_path": "train/1532.png"}
{"question": "$\\overline{AB}$ is a diameter, $AC=8$ inches, and $BC=15$ inches. Find the diameter of the circle.", "answer": "17", "image_path": "train/1533.png"}
{"question": "Find $XY$.", "answer": "21", "image_path": "train/1534.png"}
{"question": "Use parallelogram MNPR to find $w$", "answer": "3.5", "image_path": "train/1535.png"}
{"question": "Find x", "answer": "15", "image_path": "train/1536.png"}
{"question": "Find $m \\widehat{B C A}$", "answer": "180", "image_path": "train/1537.png"}
{"question": "What is the area of the triangle? Round your answer to the nearest tenth if necessary.", "answer": "161.3", "image_path": "train/1538.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "408", "image_path": "train/1539.png"}
{"question": "Find y in the figure.", "answer": "45", "image_path": "train/1540.png"}
{"question": "If $AC=14,BC=8$, and $AD=21$, find $ED$.", "answer": "12", "image_path": "train/1541.png"}
{"question": "What is the measure of $\\angle GHI$?", "answer": "110", "image_path": "train/1542.png"}
{"question": "If $\\overline{E C}$ is an altitude of $\\triangle A E D, m \\angle 1=2 x+7,$ and $m \\angle 2=3 x+13,$ find $m \\angle 1$.", "answer": "35", "image_path": "train/1543.png"}
{"question": "If $b=18,$ find $a$ ", "answer": "6 \\sqrt { 3 }", "image_path": "train/1544.png"}
{"question": "Use parallelogram MNPR to find $m \\angle NRP$", "answer": "33", "image_path": "train/1545.png"}
{"question": "Find x. ", "answer": "3 \\sqrt { 5 }", "image_path": "train/1546.png"}
{"question": "Find x", "answer": "0", "image_path": "train/1547.png"}
{"question": "$ACDF \\sim VWYZ$. Find $y$.", "answer": "3", "image_path": "train/1548.png"}
{"question": "Find $y$.", "answer": "73.5", "image_path": "train/1549.png"}
{"question": "Find $D C$ if $\\overline{D G}$ and $\\overline{J M}$ are altitudes and $\\triangle K J L \\sim \\triangle E D C$", "answer": "4", "image_path": "train/1550.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "315.2", "image_path": "train/1551.png"}
{"question": "In $\\odot X, A B=30, C D=30,$ and $m \\widehat{C Z}=40$\r\nFind CN", "answer": "15", "image_path": "train/1552.png"}
{"question": "Circles $G, J,$ and $K$ all intersect at $L$ If $G H=10,$ find GL.", "answer": "10", "image_path": "train/1553.png"}
{"question": "$\\triangle RST \\cong \\triangle ABC$. Find $y$.", "answer": "21", "image_path": "train/1554.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "164.3", "image_path": "train/1555.png"}
{"question": "Find $\\angle 4$", "answer": "60", "image_path": "train/1556.png"}
{"question": "Find x.", "answer": "8 \\sqrt { 2 }", "image_path": "train/1557.png"}
{"question": "Triangle $JKL$ is circumscribed about $\\odot R$. Find $x$.", "answer": "4", "image_path": "train/1558.png"}
{"question": "Find QS", "answer": "3", "image_path": "train/1559.png"}
{"question": "Find the measure of $\\angle 1$.", "answer": "85", "image_path": "train/1560.png"}
{"question": "If $\\overline{QR} \\| \\overline{XY}, \\overline{XQ} \\cong \\overline{QZ}$, and $QR=9.5$ units, what is the length of $\\overline{XY}$.", "answer": "19", "image_path": "train/1561.png"}
{"question": "In quadrilateral $A B C D, A C=188, B D=214$, $m \\angle B P C=70,$ and $P$ is the midpoint of $A C$ and BD. Find the perimeter of quadrilateral $A B C D .$", "answer": "561.2", "image_path": "train/1562.png"}
{"question": "Quadrilateral EFGH is a rectangle. Find $m\\angle HEF + m\\angle EFG$.", "answer": "180", "image_path": "train/1563.png"}
{"question": "Find the area of the quadrilateral.", "answer": "2829.0", "image_path": "train/1564.png"}
{"question": "In the figure, $m∠1 = 94$. Find the measure of $\\angle 5$.", "answer": "94", "image_path": "train/1565.png"}
{"question": "What is the ratio of the measure of $\\angle A C B$ to the measure of $\\angle A O B ?$", "answer": "0.5", "image_path": "train/1566.png"}
{"question": "Find the area of the kite.", "answer": "110", "image_path": "train/1567.png"}
{"question": "Find $y$.", "answer": "35", "image_path": "train/1568.png"}
{"question": "$\\Delta EFG$ is equilateral, and $\\overline{E H}$ bisects $\\angle E$. Find $x$.", "answer": "6", "image_path": "train/1569.png"}
{"question": "Find $y$ if $\\overline{AD}$ is an altitude of $\\triangle ABC$.", "answer": "48", "image_path": "train/1570.png"}
{"question": "Find $x$.", "answer": "102", "image_path": "train/1571.png"}
{"question": "parallelogram MNPQ with $m \\angle M=10 x$ and $m \\angle N=20 x$, find $\\angle P$", "answer": "60", "image_path": "train/1572.png"}
{"question": "Quadrilateral $A B C D$ is inscribed in $\\odot Z$ such that $m \\angle B Z A=104, m \\widehat{C B}=94,$ and $\\overline{A B} \\| \\overline{D C} .$\r\nFind $m \\angle B D A$", "answer": "52", "image_path": "train/1573.png"}
{"question": "For trapezoid QRTU, V and S are midpoints of the legs. If QR = 2 and VS = 7, find UT.", "answer": "12", "image_path": "train/1574.png"}
{"question": "Find x", "answer": "6", "image_path": "train/1575.png"}
{"question": "Find $m \\angle 3$.", "answer": "95", "image_path": "train/1576.png"}
{"question": "What is the area of the triangle below? Round your answer to the nearest tenth if necessary.", "answer": "171.9", "image_path": "train/1577.png"}
{"question": "In the figure, $m ∠1 = 58 $, $m ∠2 = 47 $, and $m ∠3 = 26 $. Find the measure of $∠4$.", "answer": "107", "image_path": "train/1578.png"}
{"question": "Find $x$ so that $m || n$.", "answer": "39", "image_path": "train/1579.png"}
{"question": "In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\\angle 10$.", "answer": "142", "image_path": "train/1580.png"}
{"question": "For trapezoid $J K L M, A$ and $B$ are midpoints of the legs. If $A B=57$ and $K L=21,$ find $J M$", "answer": "93", "image_path": "train/1581.png"}
{"question": "Rhombus $MNPQ$ has an area of 375 square inches. If $MP$ is 25 inches, find $NQ$.", "answer": "30", "image_path": "train/1582.png"}
{"question": "Find $x$.", "answer": "12", "image_path": "train/1583.png"}
{"question": "Find the length of $\\widehat {ZY}$. Round to the nearest hundredth.", "answer": "11.34", "image_path": "train/1584.png"}
{"question": "Find x", "answer": "45", "image_path": "train/1585.png"}
{"question": "Find z", "answer": "25", "image_path": "train/1586.png"}
{"question": " $m \\widehat{G H}=78$ Find $m\\angle 3$", "answer": "39", "image_path": "train/1587.png"}
{"question": "Find $m \\angle v$.", "answer": "76", "image_path": "train/1588.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "164", "image_path": "train/1589.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "174.4", "image_path": "train/1590.png"}
{"question": "Quadrilateral ABCD is a rectangle. Find y", "answer": "5", "image_path": "train/1591.png"}
{"question": "Use parallelogram ABCD to find $m \\angle BCF $", "answer": "49", "image_path": "train/1592.png"}
{"question": "$\\overline{AB}$ and $\\overline{CB}$ are tangent to $\\odot D$. Find the value of $x$.", "answer": "20", "image_path": "train/1593.png"}
{"question": "Find the scale factor from $W$ to $W'$.", "answer": "2", "image_path": "train/1594.png"}
{"question": "Find y", "answer": "3 \\sqrt { 2 }", "image_path": "train/1595.png"}
{"question": "The segment is tangent to the circle. Find $x$.", "answer": "3", "image_path": "train/1596.png"}
{"question": "$\\overline{E C}$ and $\\overline{A B}$ are diameters of $\\odot O$.  Find its measure of $\\widehat{EB}$.", "answer": "90", "image_path": "train/1597.png"}
{"question": "Find the measure of the altitude drawn to the hypotenuse.", "answer": "2 \\sqrt { 3 }", "image_path": "train/1598.png"}
{"question": "Circle $A$ has diameters $\\overline{D F}$ and $\\overline{P G}$\r\nIf $A G=12,$ find $L A$", "answer": "12", "image_path": "train/1599.png"}
{"question": "Find $m \\angle 1$.", "answer": "59", "image_path": "train/1600.png"}
{"question": "JKLM is a rectangle. MLPR is a rhombus. $\\angle J M K \\cong \\angle R M P$, $m \\angle J M K=55$ and  $m \\angle M R P=70 $. Find $m \\angle M P R$", "answer": "55", "image_path": "train/1601.png"}
{"question": "In quadrilateral $P Q R S, P Q=721, Q R=547$, $R S=593, P S=756,$ and $m \\angle P=58 .$ \r\nFind $Q S$", "answer": "716.7", "image_path": "train/1602.png"}
{"question": "Find the area of the sector. Round to the nearest tenth.", "answer": "67.6", "image_path": "train/1603.png"}
{"question": "Find x. Round side measures to the nearest tenth.", "answer": "2.0", "image_path": "train/1604.png"}
{"question": "Find $x$.", "answer": "75", "image_path": "train/1605.png"}
{"question": "Find the perimeter of $▱ TRVW$.", "answer": "60", "image_path": "train/1606.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth, if necessary.", "answer": "40.2", "image_path": "train/1607.png"}
{"question": "Find $AB$.", "answer": "12", "image_path": "train/1608.png"}
{"question": "If $D E=60$ and $F C=16,$ find $A B$", "answer": "68", "image_path": "train/1609.png"}
{"question": "$\\overrightarrow{BA}$ and $\\overrightarrow{BC}$ are opposite rays and $\\overrightarrow{BD}$ bisects $\\angle ABF$. If $m \\angle ABF=3x-8$ and $m \\angle ABD=x+14$, find $m \\angle ABD$.", "answer": "50", "image_path": "train/1610.png"}
{"question": "For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.", "answer": "\\frac { 5 } { 3 }", "image_path": "train/1611.png"}
{"question": "Find $KL$.", "answer": "6", "image_path": "train/1612.png"}
{"question": "ABCD is a rectangle.  If $A C=9 x-1$ and $A F=2 x+7,$ find $A F$", "answer": "13", "image_path": "train/1613.png"}
{"question": "Find $m \\angle FED$.", "answer": "82", "image_path": "train/1614.png"}
{"question": "Find the measure of $∠A$ to the nearest tenth.", "answer": "78.5", "image_path": "train/1615.png"}
{"question": "Quadrilateral $ABCD$ is a rhombus.  If $AP = 3x – 1$ and $PC = x + 9$, find $AC$.", "answer": "28", "image_path": "train/1616.png"}
{"question": "Find the area of the shaded region. Assume that the polygon is regular unless otherwise stated. Round to the nearest tenth.", "answer": "139.1", "image_path": "train/1617.png"}
{"question": "Find $m\\angle Y$", "answer": "68", "image_path": "train/1618.png"}
{"question": "Find the measure of $ \\angle 6 $ if $l  \\parallel m$  and $m \\angle 1 = 105$.", "answer": "105", "image_path": "train/1619.png"}
{"question": "Quadrilateral ABCD is shown. AC is 40 and BD is $\\frac{3}{5}$ AC . BD bisects AC. For what value of $x$ is ABCD a parallelogram.", "answer": "4", "image_path": "train/1620.png"}
{"question": "Find $m \\angle 2$.", "answer": "23", "image_path": "train/1621.png"}
{"question": "Find the area of the triangle. Round to the nearest hundredth.", "answer": "3.40", "image_path": "train/1622.png"}
{"question": "Find the area of the blue region.", "answer": "17.5", "image_path": "train/1623.png"}
{"question": "$\\overline{BC} \\| \\overline{DF}$. $AC=15$, $BD=3x-2$, $CF=3x+2$, and $AB=12$. Find $x$.", "answer": "6", "image_path": "train/1624.png"}
{"question": "Find y", "answer": "4 \\sqrt { 3 }", "image_path": "train/1625.png"}
{"question": "What is the perimeter of the triangle?", "answer": "36", "image_path": "train/1626.png"}
{"question": "Find the measure of the altitude drawn to the hypotenuse.", "answer": "5", "image_path": "train/1627.png"}
{"question": "Find the exact circumference of $\\odot P$", "answer": "13 \\pi", "image_path": "train/1628.png"}
{"question": "Find x", "answer": "20", "image_path": "train/1629.png"}
{"question": "For trapezoid QRTU, V and S are midpoints of the legs.  If RQ = 5 and VS = 11, find UT.", "answer": "17", "image_path": "train/1630.png"}
{"question": "Find $PW$, if $XZ = 18$ and $PY = 3$", "answer": "15", "image_path": "train/1631.png"}
{"question": "Find $m \\angle JLK$.", "answer": "40", "image_path": "train/1632.png"}
{"question": "In the figure, $\\overline{CP}$ is an altitude, $\\overline{CQ}$ is the angle bisector of $∠ACB$, and $R$ is the midpoint of $\\overline{AB}$. Find  $AB$ if $AR=3x+6$ and $RB = 5x - 14 $.", "answer": "72", "image_path": "train/1633.png"}
{"question": "Find $m\\angle C$", "answer": "103", "image_path": "train/1634.png"}
{"question": "Find x. Round the angle measure to the nearest degree", "answer": "72", "image_path": "train/1635.png"}
{"question": "In rhombus LMPQ, $m \\angle Q L M=2 x^{2}-10$, $m \\angle Q P M=8 x$,  and $M P=10$ . \r\nFind QL", "answer": "10", "image_path": "train/1636.png"}
{"question": "Find x", "answer": "120", "image_path": "train/1637.png"}
{"question": "Find the exact circumference of the circle.", "answer": "34 \\pi", "image_path": "train/1638.png"}
{"question": "Find x.", "answer": "5.6", "image_path": "train/1639.png"}
{"question": "Find the perimeter of the $\\triangle CBH,$ if $\\triangle CBH \\sim \\triangle FEH$, $ADEG$ is a parallelogram, $CH=7$, $FH=10, FE=11$, and $EH=6$. Rounded to the nearest tenth.", "answer": "18.9", "image_path": "train/1640.png"}
{"question": "If $\\angle R S T$ is a right angle, $\\overline{SU} \\perp \\overline{RT}$, $\\overline{UV} \\perp \\overline{ST},$ and $m \\angle RT S=47,$ find $m \\angle RSU$", "answer": "47", "image_path": "train/1641.png"}
{"question": "Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "48", "image_path": "train/1642.png"}
{"question": "Find $m \\angle 1$.", "answer": "55", "image_path": "train/1643.png"}
{"question": "Find the angle measure of $\\angle 1$.", "answer": "142", "image_path": "train/1644.png"}
{"question": "For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.", "answer": "\\frac { 3 } { 4 }", "image_path": "train/1645.png"}
{"question": "In $\\odot D, \\overline{D E} \\cong \\overline{E C}, m \\overline{C F}=60,$ and\r\n$\\overline{D E} \\perp \\overline{E C} .$ Find $m \\angle 4$", "answer": "45", "image_path": "train/1646.png"}
{"question": "What is the value of x in the figure below?", "answer": "7", "image_path": "train/1647.png"}
{"question": "Find x. Round to the nearest hundredth.", "answer": "16.93", "image_path": "train/1648.png"}
{"question": "Use rectangle LMNP, parallelogram LKMJ to solve the problem.\r\nIf $m \\angle L M P=m \\angle P M N,$ find $m \\angle P J L$", "answer": "90", "image_path": "train/1649.png"}
{"question": "Find x", "answer": "2 \\sqrt { 22 }", "image_path": "train/1650.png"}
{"question": "Find $x$ so that $ m \\parallel n $.", "answer": "15", "image_path": "train/1651.png"}
{"question": "In $\\triangle A B C, C D$ is an altitude and $m \\angle A C B=90^{\\circ}$ If $A D=12$ and $B D=3,$ find $A C$ to the nearest tenth. ", "answer": "13.4", "image_path": "train/1652.png"}
{"question": "Use parallelogram to find $y$", "answer": "63.5", "image_path": "train/1653.png"}
{"question": "Find x.", "answer": "\\sqrt { 11 }", "image_path": "train/1654.png"}
{"question": "Find x. Round the side measure to the nearest tenth.", "answer": "117.6", "image_path": "train/1655.png"}
{"question": "For trapezoid $Q R S T, A$ and $B$ are midpoints of the legs. Find $A B$", "answer": "16", "image_path": "train/1656.png"}
{"question": "Find $x$ so that $ m \\parallel n $.", "answer": "13", "image_path": "train/1657.png"}
{"question": "Find the measure of $\\angle 1$.", "answer": "55", "image_path": "train/1658.png"}
{"question": "Find $x$. $A = 96$ in$^2$.", "answer": "6.6", "image_path": "train/1659.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth.", "answer": "3.4", "image_path": "train/1660.png"}
{"question": "Find the measure of $\\angle 2$.", "answer": "110", "image_path": "train/1661.png"}
{"question": "Find the measure of $\\angle 7$.", "answer": "110", "image_path": "train/1662.png"}
{"question": "In the figure at the right, what is the value of $p$ in terms of $m$ and $n$?", "answer": "m + n - 180", "image_path": "train/1663.png"}
{"question": "Find cosA", "answer": "\\frac { 5 \\sqrt { 26 } } { 26 }", "image_path": "train/1664.png"}
{"question": "If $\\overline{PR} \\| \\overline{KL}, KN=9, LN=16,$ and $PM=2KP$, find $KP$.", "answer": "5", "image_path": "train/1665.png"}
{"question": "Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "answer": "5", "image_path": "train/1666.png"}
{"question": "Find x", "answer": "\\frac { 56 } { 5 }", "image_path": "train/1667.png"}
{"question": "Find the perimeter of the parallelogram.", "answer": "116", "image_path": "train/1668.png"}
{"question": "Trapezoid $ABCD$ has an area of 750 square meters. Find the height of $ABCD$.", "answer": "25", "image_path": "train/1669.png"}
{"question": "Find y", "answer": "3", "image_path": "train/1670.png"}
{"question": "$\\triangle RST \\cong \\triangle XYZ$. Find $x$.", "answer": "35", "image_path": "train/1671.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "288", "image_path": "train/1672.png"}
{"question": "Find the perimeter of the triangle at the right. Assume that segments that appear to be tangent are tangent.", "answer": "58", "image_path": "train/1673.png"}
{"question": "Find $CB$.", "answer": "3", "image_path": "train/1674.png"}
{"question": "Use parallelogram $JKLM$ to find $m \\angle MJK$.", "answer": "100", "image_path": "train/1675.png"}
{"question": "Find $m \\widehat {WX}$.", "answer": "66", "image_path": "train/1676.png"}
{"question": "$\\overline{JH}$ is a midsegment of $\\triangle KLM$. Find $x$.", "answer": "11", "image_path": "train/1677.png"}
{"question": "QRST is a rectangle. If $Q P=3 x+11$ and $P S=4 x+8,$ find $Q S$", "answer": "40", "image_path": "train/1678.png"}
{"question": "If PR || KL, KN = 9, LN = 16, PM = 2 KP, find KM", "answer": "15", "image_path": "train/1679.png"}
{"question": "Find $m \\angle 2$.", "answer": "52", "image_path": "train/1680.png"}
{"question": "If $A D=24,$ find $C N$", "answer": "12", "image_path": "train/1681.png"}
{"question": "Find the area of the trapezoid. ", "answer": "500", "image_path": "train/1682.png"}
{"question": "The segment is tangent to the circle. Find $x$.", "answer": "4", "image_path": "train/1683.png"}
{"question": "Parallelogram MNPQ is shown. What is the value of $x$?", "answer": "13", "image_path": "train/1684.png"}
{"question": "Find the area of the figure.", "answer": "938.4", "image_path": "train/1685.png"}
{"question": "Find the value of $x$ in the diagram", "answer": "20", "image_path": "train/1686.png"}
{"question": "Find $y$.", "answer": "72", "image_path": "train/1687.png"}
{"question": "Find $x$.", "answer": "60", "image_path": "train/1688.png"}
{"question": "Find $x$.", "answer": "11", "image_path": "train/1689.png"}
{"question": "In the figure, $m∠3 = 110$ and $m ∠ 12 = 55$. Find the measure of $∠6$.", "answer": "110", "image_path": "train/1690.png"}
{"question": "Find $m\\angle Z$", "answer": "143", "image_path": "train/1691.png"}
{"question": "Find the measure of $AC$.", "answer": "38", "image_path": "train/1692.png"}
{"question": "The height of a triangle is 5 centimeters more than its base. The area of the triangle is 52 square centimeters. Find the base.", "answer": "8", "image_path": "train/1693.png"}
{"question": "Use parallelogram JKLM to find $m \\angle JML$ if $J K=2 b+3$ and $J M=3 a$.", "answer": "80", "image_path": "train/1694.png"}
{"question": "Find $m \\angle 2$.", "answer": "106", "image_path": "train/1695.png"}
{"question": "Express the ratio of $\\sin C$ as a decimal to the nearest hundredth.", "answer": "0.60", "image_path": "train/1696.png"}
{"question": "Find y.", "answer": "10 \\sqrt { 3 }", "image_path": "train/1697.png"}
{"question": "Point $S$ is the incenter of $\\triangle JPL$. Find $m \\angle SJP$.", "answer": "37.5", "image_path": "train/1698.png"}
{"question": "Find the perimeter of the figure in feet. Round to the nearest tenth, if necessary.", "answer": "20.5", "image_path": "train/1699.png"}
{"question": "Find $m \\angle C$.", "answer": "122", "image_path": "train/1700.png"}
{"question": "Find x", "answer": "38.4", "image_path": "train/1701.png"}
{"question": "If $CN=8$. Find $DN$.", "answer": "8", "image_path": "train/1702.png"}
{"question": "Find x. Round the side measure to the nearest tenth.", "answer": "14.9", "image_path": "train/1703.png"}
{"question": "$ABCD$ is a rhombus. If $PB = 12$, $AB = 15$, and $m\\angle ABD = 24$, Find $CP$", "answer": "9", "image_path": "train/1704.png"}
{"question": "Find $m \\angle G$.", "answer": "93", "image_path": "train/1705.png"}
{"question": "Find the value of the variable $y$ in the figure.", "answer": "14", "image_path": "train/1706.png"}
{"question": "Find $RT$.", "answer": "31", "image_path": "train/1707.png"}
{"question": "Find $x$ so that the quadrilateral is a parallelogram", "answer": "2", "image_path": "train/1708.png"}
{"question": "Each pair of polygons is similar. Find ED", "answer": "5", "image_path": "train/1709.png"}
{"question": "In $\\triangle RST$, $Z$ is the centroid and $RZ=18$. Find $SZ$.", "answer": "10", "image_path": "train/1710.png"}
{"question": "The segment is tangent to the circle. Find the value of $x$.", "answer": "6", "image_path": "train/1711.png"}
{"question": "In rhombus $A B C D, A B=2 x+3$ and $B C=5 x$. Find $m \\angle B C D$ if $m \\angle A B C=83.2$", "answer": "96.8", "image_path": "train/1712.png"}
{"question": "In the figure, $m∠8 = 96$ and $m∠12 = 42$. Find the measure of $\\angle 6$.", "answer": "42", "image_path": "train/1713.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "30", "image_path": "train/1714.png"}
{"question": "Find the value of $x$ in each diagram", "answer": "37", "image_path": "train/1715.png"}
{"question": "Find $LP$.", "answer": "15", "image_path": "train/1716.png"}
{"question": "Find x. Assume that any segment that appears to be tangent is tangent.", "answer": "4", "image_path": "train/1717.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "16", "image_path": "train/1718.png"}
{"question": "Find $x$ if $\\overline{AD}$ is an altitude of $\\triangle ABC$.", "answer": "24", "image_path": "train/1719.png"}
{"question": "ABCD is a trapezoid.\r\nIf $AC = 3x – 7$ and $BD = 2x + 8$, find the value of $x$ so that ABCD is isosceles.", "answer": "15", "image_path": "train/1720.png"}
{"question": "Find x", "answer": "6 \\sqrt { 2 }", "image_path": "train/1721.png"}
{"question": "If $QT=11$, what is $QU$.", "answer": "11", "image_path": "train/1722.png"}
{"question": "Circles $G, J,$ and $K$ all intersect at $L$. If $G H=10$. Find GJ", "answer": "5", "image_path": "train/1723.png"}
{"question": "Find $x$. Assume that segments that appear to be tangent are tangent.", "answer": "21", "image_path": "train/1724.png"}
{"question": "Find $m\\angle Y$", "answer": "72", "image_path": "train/1725.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth.", "answer": "7.7", "image_path": "train/1726.png"}
{"question": "In the figure, $m∠1 = 50$ and $m∠3 = 60$. Find the measure of $\\angle 7$.", "answer": "110", "image_path": "train/1727.png"}
{"question": "Find $WZ$.", "answer": "30", "image_path": "train/1728.png"}
{"question": "Find $x$.", "answer": "40", "image_path": "train/1729.png"}
{"question": "Find the area of $▱ TRVW$.", "answer": "108 \\sqrt 3", "image_path": "train/1730.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram.", "answer": "3", "image_path": "train/1731.png"}
{"question": "Find $y$ so that each quadrilateral is a parallelogram.", "answer": "21", "image_path": "train/1732.png"}
{"question": "$m∠4 = 32$. Find the measure of $\\angle 5$.", "answer": "58", "image_path": "train/1733.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth.", "answer": "207.6", "image_path": "train/1734.png"}
{"question": "$ \\triangle WXY $  and $ \\triangle XYZ $ are isosceles and $m∠XYZ = 128$. Find the measure of $∠YZX$.", "answer": "26", "image_path": "train/1735.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "154.1", "image_path": "train/1736.png"}
{"question": "Find the perimeter of $\\triangle C P D$ if the perimeter of $\\triangle B P A$ is 12 $, B M=\\sqrt{13},$ and $C N=3 \\sqrt{13}$", "answer": "36", "image_path": "train/1737.png"}
{"question": "$UJ=9, VJ=3$, and $ZT=18$. Find $YJ$.", "answer": "4.5", "image_path": "train/1738.png"}
{"question": "If $AC = 12$ and $AB = 25$, what is the measure of $∠B$ to the nearest tenth?", "answer": "28.7", "image_path": "train/1739.png"}
{"question": "Find $x$ so that the quadrilateral is a parallelogram", "answer": "11", "image_path": "train/1740.png"}
{"question": "Find $m\\angle M$", "answer": "30", "image_path": "train/1741.png"}
{"question": "Express the ratio of $\\tan A$ as a decimal to the nearest hundredth.", "answer": "0.42", "image_path": "train/1742.png"}
{"question": "ABCD is a trapezoid.\r\nIf $m\\angle ABC = 4x + 11$ and $m\\angle DAB = 2x + 33$, find the value of $x$ so that ABCD is isosceles.", "answer": "11", "image_path": "train/1743.png"}
{"question": "Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "answer": "4.7", "image_path": "train/1744.png"}
{"question": "In the figure, $\\overline{FJ} \\cong \\overline{FH}$ and $\\overline{GF} \\cong \\overline{GH}$. If $m∠JFH=34$, find $m∠J$.", "answer": "73", "image_path": "train/1745.png"}
{"question": "Express the ratio of $\\tan P$ as a decimal to the nearest hundredth.", "answer": "1.88", "image_path": "train/1746.png"}
{"question": "Find $x$.", "answer": "80", "image_path": "train/1747.png"}
{"question": "Find z.", "answer": "20 \\sqrt { 5 }", "image_path": "train/1748.png"}
{"question": "Find y.", "answer": "12", "image_path": "train/1749.png"}
{"question": "Find the measure of $\\angle 6$ if $m∠4= m∠5$.", "answer": "44", "image_path": "train/1750.png"}
{"question": "Each pair of polygons is similar. Find x", "answer": "71.05", "image_path": "train/1751.png"}
{"question": "Find x", "answer": "2 \\sqrt { 21 }", "image_path": "train/1752.png"}
{"question": "Use rhombus XYZW with $m \\angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\\frac{5 a+1}{4}$\r\n Find  $m \\angle Y Z V$", "answer": "37", "image_path": "train/1753.png"}
{"question": "Triangle $ABC$ is similar to triangle $DEF$. Find the scale factor.\r\n", "answer": "\\frac { 2 } { 1 }", "image_path": "train/1754.png"}
{"question": "For the pair of similar figures, find the area of the green figure.", "answer": "151.25", "image_path": "train/1755.png"}
{"question": "Find $x$.", "answer": "27", "image_path": "train/1756.png"}
{"question": "Use parallelogram ABCD to find $x$", "answer": "3", "image_path": "train/1757.png"}
{"question": "Find the ratio of the area of the circle to the area of the square.", "answer": "\\frac { \\pi } { 4 }", "image_path": "train/1758.png"}
{"question": "Express the ratio of $\\cos M$ as a decimal to the nearest hundredth.", "answer": "0.92", "image_path": "train/1759.png"}
{"question": "Find the perimeter of the figure.", "answer": "48", "image_path": "train/1760.png"}
{"question": "Find the area of the shaded region formed by the circle and regular polygon. Round to the nearest tenth.", "answer": "2.5", "image_path": "train/1761.png"}
{"question": "find $cosS$", "answer": "0.8", "image_path": "train/1762.png"}
{"question": "Triangle $LMN$ is equilateral, and $\\overline{MP}$ bisects $\\overline{LN}$. Find $x$.", "answer": "3", "image_path": "train/1763.png"}
{"question": "If the polygon shown is regular, what is $m\\angle ABC$", "answer": "140", "image_path": "train/1764.png"}
{"question": "If $LN=12.4$, what is $JM$?", "answer": "6.2", "image_path": "train/1765.png"}
{"question": "Find $YZ$ of isosceles $\\triangle XYZ$", "answer": "7", "image_path": "train/1766.png"}
{"question": "Find y.", "answer": "8 \\sqrt { 3 }", "image_path": "train/1767.png"}
{"question": "Find x", "answer": "22.6", "image_path": "train/1768.png"}
{"question": "Solve for $x$ in the figure below.", "answer": "31", "image_path": "train/1769.png"}
{"question": "Find the perimeter of the figure.", "answer": "32", "image_path": "train/1770.png"}
{"question": "Find $m \\angle W$", "answer": "62", "image_path": "train/1771.png"}
{"question": "Solve for x in the figure.", "answer": "8", "image_path": "train/1772.png"}
{"question": "Find $x$.", "answer": "13", "image_path": "train/1773.png"}
{"question": "If $\\overline{M N} \\| \\overline{P Q}$, use a proportion to find the value of $x$. ", "answer": "10", "image_path": "train/1774.png"}
{"question": "If $\\overline{PR} \\| \\overline{WX}, WX=10, XY=6, WY=8, RY=5,$ and $PS=3,$ find $SY$.", "answer": "4", "image_path": "train/1775.png"}
{"question": "Find $\\angle 3$", "answer": "110", "image_path": "train/1776.png"}
{"question": "Find z.", "answer": "2 \\sqrt { 15 }", "image_path": "train/1777.png"}
{"question": "If $m\\angle XZY = 3x + 6$ and $m\\angle XZW = 5x - 12$, find $m\\angle YXZ$.", "answer": "48", "image_path": "train/1778.png"}
{"question": "Find $m \\widehat {SU}$.", "answer": "22", "image_path": "train/1779.png"}
{"question": "Find the measure of $\\angle 1$.", "answer": "123", "image_path": "train/1780.png"}
{"question": "Find the measure of $\\angle 1$ if $m \\angle D G F=53$ and $m \\angle A G C=40$.", "answer": "37", "image_path": "train/1781.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram.", "answer": "22", "image_path": "train/1782.png"}
{"question": "Find $x$.", "answer": "6", "image_path": "train/1783.png"}
{"question": "Find $RT$.", "answer": "24", "image_path": "train/1784.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "8", "image_path": "train/1785.png"}
{"question": "$ABCD$ is a rhombus. If $PB = 12$, $AB = 15$, and $m\\angle ABD = 24$.  Find $AP$", "answer": "9", "image_path": "train/1786.png"}
{"question": "Find $y$ in the figure.", "answer": "45", "image_path": "train/1787.png"}
{"question": "Find x. Round to the nearest tenth.", "answer": "8.0", "image_path": "train/1788.png"}
{"question": "Find $m \\angle B$.", "answer": "92", "image_path": "train/1789.png"}
{"question": "Find x.", "answer": "\\frac { 14 \\sqrt { 3 } } { 3 }", "image_path": "train/1790.png"}
{"question": "Quadrilateral $A B C D$ is inscribed in $\\odot Z$ such that $m \\angle B Z A=104, m \\widehat{C B}=94,$ and $\\overline{A B} \\| \\overline{D C} .$\r\nFind $m \\widehat{B A}$", "answer": "104", "image_path": "train/1791.png"}
{"question": "Find $m \\angle Z$.", "answer": "80", "image_path": "train/1792.png"}
{"question": "$H$ is the incenter of $\\triangle ABC$. Find $BD$.", "answer": "7 \\sqrt 3", "image_path": "train/1793.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "9", "image_path": "train/1794.png"}
{"question": "$\\overline{JH}, \\overline{JP},$ and $\\overline{PH}$ are midsegments of $\\triangle KLM$. Find $x$.", "answer": "1.35", "image_path": "train/1795.png"}
{"question": "What is the area of the figure? Round to the nearest tenth.", "answer": "346.4", "image_path": "train/1796.png"}
{"question": "Find x. Round to the nearest hundredth.", "answer": "15.20", "image_path": "train/1797.png"}
{"question": "Find x. Round the side measure to the nearest tenth.", "answer": "13.1", "image_path": "train/1798.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "56", "image_path": "train/1799.png"}
{"question": "If $AB=6,BC=4$, and $AE=9$, find $ED$.", "answer": "6", "image_path": "train/1800.png"}
{"question": "Find $m \\angle 1$.", "answer": "123", "image_path": "train/1801.png"}
{"question": "Find $m \\angle JMK$.", "answer": "102", "image_path": "train/1802.png"}
{"question": "Find x.", "answer": "22", "image_path": "train/1803.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "310", "image_path": "train/1804.png"}
{"question": "In the right triangle, what is $A B$ if $B C=6 ?$", "answer": "4 \\sqrt { 3 }", "image_path": "train/1805.png"}
{"question": "Find $m \\angle C G D$", "answer": "150", "image_path": "train/1806.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram", "answer": "41", "image_path": "train/1807.png"}
{"question": "If XN = t - 2, NZ = t + 1, XM = 2, and XY = 10, solve for t", "answer": "3", "image_path": "train/1808.png"}
{"question": "Find $m\\angle D$", "answer": "74", "image_path": "train/1809.png"}
{"question": "Find $x$.", "answer": "6", "image_path": "train/1810.png"}
{"question": "Find $m \\angle DAB$.", "answer": "125", "image_path": "train/1811.png"}
{"question": "Find the measure of $\\angle 3$ in the figure.", "answer": "25", "image_path": "train/1812.png"}
{"question": "Find $x$.", "answer": "127", "image_path": "train/1813.png"}
{"question": "Find $LN$.", "answer": "29", "image_path": "train/1814.png"}
{"question": "Find x. Assume that any segment that appears to be tangent is tangent.", "answer": "8", "image_path": "train/1815.png"}
{"question": "Each pair of polygons is similar. Find BC", "answer": "8", "image_path": "train/1816.png"}
{"question": "The degree measures of minor arc $\\widehat{A C}$ and major arc $\\widehat{A D C}$ are $x$ and $y$ respectively. If $m∠ABC = 70°$, find $y$.", "answer": "250", "image_path": "train/1817.png"}
{"question": "Find $h$.", "answer": "6", "image_path": "train/1818.png"}
{"question": "Find the measure of $m∠C$.", "answer": "70", "image_path": "train/1819.png"}
{"question": "Find $m \\angle MRP$.", "answer": "60", "image_path": "train/1820.png"}
{"question": "Find $F B$ if $\\overline{S A}$ and $\\overline{F B}$ are altitudes and $\\triangle R S T \\sim \\triangle E F G$", "answer": "2", "image_path": "train/1821.png"}
{"question": "WXYZ is a square. If $WT = 3$, Find $XY$", "answer": "3 \\sqrt { 2 }", "image_path": "train/1822.png"}
{"question": "Find x. Round side measures to the nearest tenth.", "answer": "22.8", "image_path": "train/1823.png"}
{"question": "Find $QR$.", "answer": "25", "image_path": "train/1824.png"}
{"question": "Find $m \\angle 1$.", "answer": "55", "image_path": "train/1825.png"}
{"question": "In $\\odot G, m \\angle A G B=30$ and $\\overline{C G} \\perp \\overline{G D}$.\r\nFind $m \\widehat{F D}$", "answer": "30", "image_path": "train/1826.png"}
{"question": "Find $m \\angle SRT$.", "answer": "65", "image_path": "train/1827.png"}
{"question": "Find AB", "answer": "3.6", "image_path": "train/1828.png"}
{"question": "Each triangle in the figure is a $30^{\\circ}-60^{\\circ}-90^{\\circ}$ triangle. Find $x$", "answer": "2.25", "image_path": "train/1829.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "70.9", "image_path": "train/1830.png"}
{"question": "A regular hexagon is inscribed in a circle with a diameter of 14. Find the area of the red segment.", "answer": "4.44", "image_path": "train/1831.png"}
{"question": "Find $x$.", "answer": "72", "image_path": "train/1832.png"}
{"question": "$\\odot J \\cong \\odot K$ and $\\widehat {MN} \\cong \\widehat {PQ}$. Find $PQ$.", "answer": "17", "image_path": "train/1833.png"}
{"question": "Find $YZ$.", "answer": "4", "image_path": "train/1834.png"}
{"question": "Find $z$ in the figure.", "answer": "22", "image_path": "train/1835.png"}
{"question": "Find $VS$.", "answer": "20", "image_path": "train/1836.png"}
{"question": "Find the angle measure of $\\angle4$.", "answer": "52", "image_path": "train/1837.png"}
{"question": "Find $m\\angle P$", "answer": "120", "image_path": "train/1838.png"}
{"question": "Find the area of the regular polygon. Round to the nearest tenth.", "answer": "62.4", "image_path": "train/1839.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "10", "image_path": "train/1840.png"}
{"question": "Find $y$ so that each quadrilateral is a parallelogram.", "answer": "6", "image_path": "train/1841.png"}
{"question": "$a=8, b=15,$ and $c=17$ find $cosB$", "answer": "0.47", "image_path": "train/1842.png"}
{"question": "In $\\odot F$, if $DA=7.4$, what is $EF$?", "answer": "3.7", "image_path": "train/1843.png"}
{"question": "Refer to the figure at the right. Find the value of $y$ if $ p \\parallel q $.", "answer": "105", "image_path": "train/1844.png"}
{"question": "Find $m \\widehat {PM}$.", "answer": "144", "image_path": "train/1845.png"}
{"question": "Find x. Round to the nearest tenth.", "answer": "17.7", "image_path": "train/1846.png"}
{"question": "Find $m \\angle 4$.", "answer": "15", "image_path": "train/1847.png"}
{"question": "Use parallelogram NQRM to find w", "answer": "12", "image_path": "train/1848.png"}
{"question": "Find $x$ so that the quadrilateral is a parallelogram.", "answer": "4", "image_path": "train/1849.png"}
{"question": "Find $x$ so that each quadrilateral is a parallelogram.", "answer": "8", "image_path": "train/1850.png"}
{"question": "$H$ is the incenter of $\\triangle ABC$. Find $DH$.", "answer": "7", "image_path": "train/1851.png"}
{"question": "Find the measure of $\\angle 2$ if $m∠DGF = 53$ and $m∠AGC = 40$.", "answer": "50", "image_path": "train/1852.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "3108", "image_path": "train/1853.png"}
{"question": "Find $y$ so that each quadrilateral is a parallelogram.", "answer": "7", "image_path": "train/1854.png"}
{"question": "In the figure, $m ∠ 12 = 64$. Find the measure of $ \\angle 13$.", "answer": "64", "image_path": "train/1855.png"}
{"question": "Find x.", "answer": "10", "image_path": "train/1856.png"}
{"question": "Find the measure of $ \\angle 4 $ if $l  \\parallel m$  and $m \\angle 1 = 105$.", "answer": "75", "image_path": "train/1857.png"}
{"question": "In rhombus LMPQ, $m \\angle Q L M=2 x^{2}-10$, $m \\angle Q P M=8 x$,  and $M P=10$ . \r\nFind $m \\angle L P Q$", "answer": "20", "image_path": "train/1858.png"}
{"question": "Points $S$, $T$, and $U$ are the midpoints of $\\overline{DE}$, $\\overline{EF}$, and $\\overline{DF}$, respectively. Find $z$.", "answer": "0.575", "image_path": "train/1859.png"}
{"question": "Find $x$ so that the quadrilateral is a parallelogram.", "answer": "40", "image_path": "train/1860.png"}
{"question": "Find $m \\angle AEB$.", "answer": "109", "image_path": "train/1861.png"}
{"question": "In $\\odot T, Z V=1,$ and $T W=13$. Find XV", "answer": "5", "image_path": "train/1862.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "29.2", "image_path": "train/1863.png"}
{"question": "Use parallelogram to find $z$", "answer": "2", "image_path": "train/1864.png"}
{"question": "In $\\odot F$, $GK=14$ and $m \\widehat{GHK}=142$. Find $JK$.", "answer": "7", "image_path": "train/1865.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth, if necessary.", "answer": "284.0", "image_path": "train/1866.png"}
{"question": "Find $x$.", "answer": "107", "image_path": "train/1867.png"}
{"question": "$\\overline{GJ}$ is a diameter of $\\odot K$. Find $m \\widehat {GH}$.", "answer": "122", "image_path": "train/1868.png"}
{"question": "Find $m \\angle ACD$.", "answer": "44", "image_path": "train/1869.png"}
{"question": "Find x.", "answer": "6", "image_path": "train/1870.png"}
{"question": "In the figure, $m ∠ 12 = 64$. Find the measure of $ \\angle 4$.", "answer": "64", "image_path": "train/1871.png"}
{"question": "Find $XA$.", "answer": "4", "image_path": "train/1872.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "338.4", "image_path": "train/1873.png"}
{"question": "For the pair of similar figures, use the given areas to find $x$.", "answer": "35", "image_path": "train/1874.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent. ", "answer": "15", "image_path": "train/1875.png"}
{"question": "In $\\triangle ABC$, $\\overline{AD}$ and $\\overline{DC}$ are angle bisectors and $m \\angle B=76$. What is the measure of $\\angle ADC $?", "answer": "128", "image_path": "train/1876.png"}
{"question": "Find $\\angle W$", "answer": "134", "image_path": "train/1877.png"}
{"question": "The area $A$ of the shaded region is given. Find $x$. $A = 128$ ft$^2$ .", "answer": "9.8", "image_path": "train/1878.png"}
{"question": "Find the ratio of the area of $ \\triangle ABC$ to the area of square $BCDE$.", "answer": "\\frac { \\sqrt 3 } { 4 } : 1", "image_path": "train/1879.png"}
{"question": "Quadrilateral MNOP is a rectangle. If $M O=6 x+14$ and $P N=9 x+5,$ find $x$", "answer": "3", "image_path": "train/1880.png"}
{"question": "Find y", "answer": "28", "image_path": "train/1881.png"}
{"question": "$MC=7,RM=4$, and $AT=16$. Find $SC$.", "answer": "10.5", "image_path": "train/1882.png"}
{"question": "Find $m \\angle Y$.", "answer": "60", "image_path": "train/1883.png"}
{"question": "Find the value of x.", "answer": "95", "image_path": "train/1884.png"}
{"question": "Find the perimeter of the triangle. Round to the nearest tenth if necessary.", "answer": "80.0", "image_path": "train/1885.png"}
{"question": "Find $\\sin x$", "answer": "\\frac { 2 \\sqrt { 2 } } { 5 }", "image_path": "train/1886.png"}
{"question": "Suppose $C E=5.2$ inches. Find the diameter of the circle.", "answer": "10.4", "image_path": "train/1887.png"}
{"question": "Use the Pythagorean Theorem to find the length of the hypotenuse of each right triangle.", "answer": "\\sqrt { 34 }", "image_path": "train/1888.png"}
{"question": "Find the measure of the altitude drawn to the hypotenuse.", "answer": "\\sqrt { 147 }", "image_path": "train/1889.png"}
{"question": "Find WX", "answer": "10", "image_path": "train/1890.png"}
{"question": "Find the perimeter of each polygon for the given information.\r\n$S T=18,$ radius of $\\odot P=5$", "answer": "58.5", "image_path": "train/1891.png"}
{"question": "Find $m \\angle 1$.", "answer": "26", "image_path": "train/1892.png"}
{"question": "In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\\angle 12$.", "answer": "118", "image_path": "train/1893.png"}
{"question": "The segment is tangent to the circle. Find $x$.", "answer": "1", "image_path": "train/1894.png"}
{"question": "Find y.", "answer": "10 \\sqrt { 5 }", "image_path": "train/1895.png"}
{"question": "Find x", "answer": "4 \\sqrt { 74 }", "image_path": "train/1896.png"}
{"question": "$m \\angle B=76$. The measure of $\\angle A$ is half the measure of $\\angle B$. What is $m \\angle C$?", "answer": "66", "image_path": "train/1897.png"}
{"question": "In $\\triangle PQR$, $ZQ=3a-11$, $ZP=a+5$, $PY=2 c-1$, $YR=4 c-11$, $m \\angle PRZ=4 b-17$, $m \\angle ZRQ=3 b-4$, $m \\angle QYR=7 b+6$, and $m \\angle PXR=2 a+10$. $\\overline{PX}$ is an altitude of $ \\triangle PQR$. Find $a$.", "answer": "40", "image_path": "train/1898.png"}
{"question": "If CDFG is a kite, find $m\\angle D$", "answer": "122", "image_path": "train/1899.png"}
{"question": "Find $x$.", "answer": "2", "image_path": "train/1900.png"}
{"question": "In $\\odot F$, $GK=14$ and $m \\widehat{GHK}=142$. Find $m \\widehat {KM}$.", "answer": "109", "image_path": "train/1901.png"}
{"question": "Find x. Round the side measure to the nearest tenth.", "answer": "8.3", "image_path": "train/1902.png"}
{"question": "Find the perimeter of the triangle.", "answer": "100.4", "image_path": "train/1903.png"}
{"question": "Find x.", "answer": "3 \\sqrt { 29 }", "image_path": "train/1904.png"}
{"question": "Each pair of polygons is similar. Find CE", "answer": "11.4", "image_path": "train/1905.png"}
{"question": "Find $RS$.", "answer": "31", "image_path": "train/1906.png"}
{"question": "Find the value of $s$ in the parallelogram.", "answer": "13", "image_path": "train/1907.png"}
{"question": "Find x.", "answer": "12.0", "image_path": "train/1908.png"}
{"question": "For the pair of similar figures, find the area of the green figure.", "answer": "12.5", "image_path": "train/1909.png"}
{"question": "Find x. Round side measures to the nearest tenth.", "answer": "35.1", "image_path": "train/1910.png"}
{"question": "Find $x$ if $\\triangle JMN$ is an isosceles triangle with $\\overline{JM} \\cong \\overline{M N}$.", "answer": "4", "image_path": "train/1911.png"}
{"question": "Find x", "answer": "39.8", "image_path": "train/1912.png"}
{"question": "$\\Delta DFG$  and $\\Delta F G H$ are isosceles, $m \\angle FDH=28$ and$\\overline{DG} \\cong \\overline{FG} \\cong \\overline{FH}$. Find the measure of $\\angle DFG$. ", "answer": "28", "image_path": "train/1913.png"}
{"question": "Use parallelogram to find $x$", "answer": "79", "image_path": "train/1914.png"}
{"question": "If $\\overline{TU} \\perp \\overline{UV}$ and $\\overline{UV} \\perp \\overline{VW}$, find $m \\angle 1$.", "answer": "45", "image_path": "train/1915.png"}
{"question": "If $\\angle R S T$ is a right angle, $\\overline{SU} \\perp \\overline{RT}$, $\\overline{UV} \\perp \\overline{ST},$ and $m \\angle RT S=47,$ find $m \\angle SUV$", "answer": "47", "image_path": "train/1916.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth.", "answer": "10.0", "image_path": "train/1917.png"}
{"question": "Find $x$ so that the quadrilateral is a parallelogram.", "answer": "4", "image_path": "train/1918.png"}
{"question": "Find x.", "answer": "6 \\sqrt { 2 }", "image_path": "train/1919.png"}
{"question": "Find $m \\widehat {GJF}$.", "answer": "196", "image_path": "train/1920.png"}
{"question": "Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.", "answer": "4", "image_path": "train/1921.png"}
{"question": "$P$ is the incenter of $\\triangle AEC$. Find $DE$. Rounded to the nearest hundredth.", "answer": "13.11", "image_path": "train/1922.png"}
{"question": "Express the ratio of $\\tan X$ as a decimal to the nearest hundredth.", "answer": "3.43", "image_path": "train/1923.png"}
{"question": "Find $x$.", "answer": "3", "image_path": "train/1924.png"}
{"question": "Use parallelogram to  find $a$", "answer": "2", "image_path": "train/1925.png"}
{"question": "The segment is tangent to the circle. Find $x$.", "answer": "4", "image_path": "train/1926.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth.", "answer": "61.7", "image_path": "train/1927.png"}
{"question": "The segment is tangent to the circle. Find $x$ to the nearest hundredth.", "answer": "8.06", "image_path": "train/1928.png"}
{"question": "Find x.", "answer": "20", "image_path": "train/1929.png"}
{"question": "Find $x$.", "answer": "11", "image_path": "train/1930.png"}
{"question": "Find the perimeter of the figure.", "answer": "36", "image_path": "train/1931.png"}
{"question": "Find the exact value of $DE,$ given $AD=12$ and $BD=4$", "answer": "2 \\sqrt { 3 }", "image_path": "train/1932.png"}
{"question": "In the figure, $m∠3 = 43$. Find the measure of $\\angle 16$.", "answer": "137", "image_path": "train/1933.png"}
{"question": "Find $JK$.", "answer": "12", "image_path": "train/1934.png"}
{"question": "In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\\angle 4$.", "answer": "62", "image_path": "train/1935.png"}
{"question": "WXYZ is a parallelogram. Find $m \\angle Y Z W$ ", "answer": "115", "image_path": "train/1936.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "727.5", "image_path": "train/1937.png"}
{"question": "Find the area of the quadrilateral.", "answer": "260", "image_path": "train/1938.png"}
{"question": "Find x", "answer": "12", "image_path": "train/1939.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "60.1", "image_path": "train/1940.png"}
{"question": "Find x.", "answer": "12", "image_path": "train/1941.png"}
{"question": "Find $m \\angle TQR$.", "answer": "43", "image_path": "train/1942.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "8", "image_path": "train/1943.png"}
{"question": "Quadrilateral $ABCD$ is a rhombus. If $AB = 14$, find $BC$.", "answer": "14", "image_path": "train/1944.png"}
{"question": "Find the measure of $\\angle 2$ if $m∠4= m∠5$.", "answer": "53", "image_path": "train/1945.png"}
{"question": "Find x. Round the side measure to the nearest tenth.", "answer": "6.1", "image_path": "train/1946.png"}
{"question": "For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure. ", "answer": "\\frac { 3 } { 7 }", "image_path": "train/1947.png"}
{"question": "Find x.", "answer": "6", "image_path": "train/1948.png"}
{"question": "Find $y$.", "answer": "2", "image_path": "train/1949.png"}
{"question": "Find the measure of $ST$ of equilateral triangle $RST$ if $RS = x + 9$, $ST = 2x$, and $RT = 3x - 9$.", "answer": "18", "image_path": "train/1950.png"}
{"question": "Use parallelogram NQRM to find QR", "answer": "15", "image_path": "train/1951.png"}
{"question": "Equilateral pentagon $P Q R S T$ is inscribed in $\\odot U$.\r\nFind $m \\angle P T S$", "answer": "144", "image_path": "train/1952.png"}
{"question": "In $\\odot X, A B=30, C D=30,$ and $m \\widehat{C Z}=40$\r\nFind AM", "answer": "15", "image_path": "train/1953.png"}
{"question": "Use parallelogram ABCD to find $x$", "answer": "5", "image_path": "train/1954.png"}
{"question": "Find $x$ so that $ m \\parallel n $.", "answer": "9", "image_path": "train/1955.png"}
{"question": "Find $x$ so that each quadrilateral is a parallelogram.", "answer": "8", "image_path": "train/1956.png"}
{"question": "If $a=10 \\sqrt{3},$ find $C E$ ", "answer": "15", "image_path": "train/1957.png"}
{"question": "Find the measure of $\\angle 4$ if $m \\angle D G F=53$ and $m \\angle A G C=40$.", "answer": "40", "image_path": "train/1958.png"}
{"question": "Polygon $BCDE$ $\\cong$ polygon $RSTU$. Find $w$.", "answer": "10", "image_path": "train/1959.png"}
{"question": "If $\\overline{K H}$ is parallel to $\\overline{JI}$, find the measure of  $\\angle 1$", "answer": "66", "image_path": "train/1960.png"}
{"question": "Each pair of polygons is similar. Find x", "answer": "10", "image_path": "train/1961.png"}
{"question": "Find x. Round to the nearest tenth.\r\n", "answer": "7.1", "image_path": "train/1962.png"}
{"question": "Find $m \\angle 3$.", "answer": "68", "image_path": "train/1963.png"}
{"question": "Find $JL$, if $KP = 4$ and $PM = 7$", "answer": "11", "image_path": "train/1964.png"}
{"question": "Find $x$ so that each quadrilateral is a parallelogram.", "answer": "6", "image_path": "train/1965.png"}
{"question": "Find x.", "answer": "9 \\sqrt { 3 }", "image_path": "train/1966.png"}
{"question": "Use parallelogram PQRS to find $m\\angle R$", "answer": "52", "image_path": "train/1967.png"}
{"question": "Find $x$.", "answer": "102", "image_path": "train/1968.png"}
{"question": "Find $AB$.", "answer": "10", "image_path": "train/1969.png"}
{"question": "$ABCD \\sim QSRP$. Find $x$.", "answer": "63", "image_path": "train/1970.png"}
{"question": "The two polygons are similar. Then find y.", "answer": "20.5", "image_path": "train/1971.png"}
{"question": "Solve for $x$.", "answer": "6", "image_path": "train/1972.png"}
{"question": "Find x", "answer": "5 \\sqrt { 2 }", "image_path": "train/1973.png"}
{"question": "In the figure, a regular polygon is inscribed in a circle. Find the measure of a central angle.", "answer": "72", "image_path": "train/1974.png"}
{"question": "Find the perimeter of the figure. Round to the nearest tenth if necessary.", "answer": "31.4", "image_path": "train/1975.png"}
{"question": "Find the measure of $\\angle 2$ in the figure.", "answer": "105", "image_path": "train/1976.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth, if necessary.", "answer": "322.0", "image_path": "train/1977.png"}
{"question": "Quadrilateral $WXYZ$ is a rectangle. Find the measure of $\\angle 12$ if $m∠1 = 30$.", "answer": "120", "image_path": "train/1978.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "6", "image_path": "train/1979.png"}
{"question": "$RP=3.5$ and $JP=9$. Find $PS$.", "answer": "4.5", "image_path": "train/1980.png"}
{"question": "Polygon $BCDE$ $\\cong$ polygon $RSTU$. Find $z$.", "answer": "3", "image_path": "train/1981.png"}
{"question": "Find z.", "answer": "8", "image_path": "train/1982.png"}
{"question": "In the figure, $m∠1 = 123$. Find the measure of $\\angle 16$.", "answer": "57", "image_path": "train/1983.png"}
{"question": "In $\\triangle JLP$, $m \\angle JMP=3 x-6$, $JK=3y-2$, and $LK=5y-8$. Find $LK$ if $\\overline{PK}$ is a median.\r\n", "answer": "7", "image_path": "train/1984.png"}
{"question": "Given figure $A B C D$, with $\\overline{A B} \\| \\overline{D C}, m \\angle B=60, m \\angle D=45, B C=8$\r\nand $A B=24,$ find the perimeter.", "answer": "52 + 4 \\sqrt { 3 } + 4 \\sqrt { 6 }", "image_path": "train/1985.png"}
{"question": "For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure.", "answer": "\\frac { 5 } { 6 }", "image_path": "train/1986.png"}
{"question": "Find $x$.", "answer": "5", "image_path": "train/1987.png"}
{"question": "Circle $W$ has a radius of 4 units, $\\odot Z$ has a radius of 7 units, and $X Y=2 .$ Find $Y Z$", "answer": "5", "image_path": "train/1988.png"}
{"question": "Find $y$.", "answer": "3", "image_path": "train/1989.png"}
{"question": "Find $m\\angle 3$.", "answer": "12", "image_path": "train/1990.png"}
{"question": "Find x", "answer": "4 \\sqrt { 29 }", "image_path": "train/1991.png"}
{"question": "$ABCD \\sim QSRP$. Find $y$.", "answer": "32", "image_path": "train/1992.png"}
{"question": "Find the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "22.7", "image_path": "train/1993.png"}
{"question": "Find $x$.", "answer": "114", "image_path": "train/1994.png"}
{"question": "In the figure, $m ∠9 = 75$. Find the measure of $\\angle 8$.", "answer": "105", "image_path": "train/1995.png"}
{"question": "In H, the diameter is $18$, $LM = 12$, and $m \\widehat {LM} = 84$. Find $m \\widehat {LK}$.", "answer": "42", "image_path": "train/1996.png"}
{"question": "Find x", "answer": "42.5", "image_path": "train/1997.png"}
{"question": "Find $m \\angle H$.", "answer": "54", "image_path": "train/1998.png"}
{"question": "Find $h$.", "answer": "4 \\sqrt 2", "image_path": "train/1999.png"}
{"question": "Find x. Round to the nearest degree.", "answer": "63", "image_path": "train/2000.png"}
{"question": "Find $m \\angle F$.", "answer": "30", "image_path": "train/2001.png"}
{"question": "In $\\triangle ABC, \\overline{BD}$ is a median. If $AD=3x+5$ and $CD=5x-1,$ find $AC$.", "answer": "28", "image_path": "train/2002.png"}
{"question": "WXYZ is a parallelogram. Find $m \\angle X W Z$ ", "answer": "65", "image_path": "train/2003.png"}
{"question": "In $\\odot R, S U=20, Y W=20,$ and $m \\widehat{Y X}=45$.\r\nFind $m\\widehat{S U}$", "answer": "90", "image_path": "train/2004.png"}
{"question": "isosceles trapezoid TWYZ with $\\angle Z \\cong \\angle Y, m \\angle Z=30 x$, $\\angle T \\cong \\angle W,$ and $m \\angle T=20 x$, find Z", "answer": "108", "image_path": "train/2005.png"}
{"question": "Find $y$ in the figure.", "answer": "28", "image_path": "train/2006.png"}
{"question": "Find $y$.", "answer": "1", "image_path": "train/2007.png"}
{"question": "Refer to trapezoid $CDFG$ with median $\\overline{HE}$. Let $\\overline{WX}$ be the median of $CDEH$. Find $WX$.", "answer": "42", "image_path": "train/2008.png"}
{"question": "Find the measure of the altitude drawn to the hypotenuse", "answer": "12", "image_path": "train/2009.png"}
{"question": "Find x", "answer": "17.1", "image_path": "train/2010.png"}
{"question": "Find $\\angle B$ of quadrilateral ABCD", "answer": "90", "image_path": "train/2011.png"}
{"question": "Each pair of polygons is similar. Find y", "answer": "7", "image_path": "train/2012.png"}
{"question": "Find x. Assume that any segment that appears to be tangent is tangent.", "answer": "210", "image_path": "train/2013.png"}
{"question": "Find x.", "answer": "\\frac { 3 } { 2 } \\sqrt { 3 }", "image_path": "train/2014.png"}
{"question": "$a=8, b=15,$ and $c=17$, find $sinA$", "answer": "0.47", "image_path": "train/2015.png"}
{"question": "Find $y$.", "answer": "11", "image_path": "train/2016.png"}
{"question": "In $\\odot O, \\overline{E C}$ and $\\overline{A B}$ are diameters, and $\\angle B O D \\cong \\angle D O E \\cong \\angle E O F \\cong \\angle F O A$\r\nFind $m\\widehat{B C}$", "answer": "90", "image_path": "train/2017.png"}
{"question": "Find the value of $h$.", "answer": "84.85", "image_path": "train/2018.png"}
{"question": "Find the measure of the altitude drawn to the hypotenuse.", "answer": "\\sqrt { 612 }", "image_path": "train/2019.png"}
{"question": "Find y.", "answer": "7", "image_path": "train/2020.png"}
{"question": "Find x", "answer": "22", "image_path": "train/2021.png"}
{"question": "Find the variable of $d$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "16.9", "image_path": "train/2022.png"}
{"question": "Find $x$.", "answer": "28", "image_path": "train/2023.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth, if necessary.", "answer": "167.1", "image_path": "train/2024.png"}
{"question": "Find the length of $FG$", "answer": "39", "image_path": "train/2025.png"}
{"question": "In the figure, $\\overline{A B} \\parallel \\overline{C E} .$ If $D A=6,$ what is $D B ?$", "answer": "6", "image_path": "train/2026.png"}
{"question": "In the figure, $QR \\| TS$, $QT \\| RS$, and $m \\angle 1=131$. Find the measure of $\\angle 2$. ", "answer": "49", "image_path": "train/2027.png"}
{"question": "The area of a circle is 20 $\\pi$ square centimeters. What is its circumference?", "answer": "4 \\sqrt 5 \\pi", "image_path": "train/2028.png"}
{"question": "Find x", "answer": "45", "image_path": "train/2029.png"}
{"question": "Find x.", "answer": "6", "image_path": "train/2030.png"}
{"question": "Rhombus $A B C D$ is circumscribed about $\\odot P$ and has a perimeter of 32 Find $x$", "answer": "5", "image_path": "train/2031.png"}
{"question": "Find the area of the figure in feet. Round to the nearest tenth, if necessary.", "answer": "31.2", "image_path": "train/2032.png"}
{"question": "Find $m \\angle MNP$.", "answer": "130", "image_path": "train/2033.png"}
{"question": "In $\\odot S$, find $PR$.", "answer": "12", "image_path": "train/2034.png"}
{"question": "Find x.", "answer": "12", "image_path": "train/2035.png"}
{"question": "Refer to the triangle shown below. Find $z$ to the nearest tenth.", "answer": "\\frac { 5 } { 2 } \\sqrt { 41 }", "image_path": "train/2036.png"}
{"question": "In $\\triangle EFG, \\overline{HL} \\parallel \\overline{EF}, EH=9, HG=21,$ and $FL=6 .$ Find $LG$", "answer": "14", "image_path": "train/2037.png"}
{"question": "Find $x$.", "answer": "3", "image_path": "train/2038.png"}
{"question": "Quadrilateral $ABDC$  is a rectangle. Find $m \\angle 6$ if $ m\\angle 1 = 38$.", "answer": "38", "image_path": "train/2039.png"}
{"question": "Find the area of the kite.", "answer": "52.5", "image_path": "train/2040.png"}
{"question": "In the figure, $ \\overline{GK} \\cong \\overline{GH}$ and $ \\overline{HK} \\cong \\overline{KJ}$. If $m \\angle HGK=28$, find $m \\angle HJK$.", "answer": "38", "image_path": "train/2041.png"}
{"question": "Find AS", "answer": "8", "image_path": "train/2042.png"}
{"question": "Find x. Assume that any segment that appears to be tangent is tangent.", "answer": "13", "image_path": "train/2043.png"}
{"question": "Find y.", "answer": "3 \\sqrt { 5 }", "image_path": "train/2044.png"}
{"question": "Find the exact circumference of each circle.", "answer": "5 \\pi", "image_path": "train/2045.png"}
{"question": "Find $m \\angle 1$.", "answer": "85", "image_path": "train/2046.png"}
{"question": "The area $A$ of the shaded region is given. Find $x$. $A = 94$ in$^2$ .", "answer": "55.0", "image_path": "train/2047.png"}
{"question": "Find $x$ if $\\overline{PS}$ is a median of $\\triangle PQR$.", "answer": "2", "image_path": "train/2048.png"}
{"question": "The diameters of $\\odot A, \\odot B,$ and $\\odot C$ are $8$ inches, $18$ inches, and $11$ inches, respectively. Find $FG$.", "answer": "14", "image_path": "train/2049.png"}
{"question": "Find y.", "answer": "\\frac { 25 } { 14 }", "image_path": "train/2050.png"}
{"question": "If $\\overline{K H}$ is parallel to $\\overline{JI}$, find the measure of  $\\angle 2$", "answer": "54", "image_path": "train/2051.png"}
{"question": "If $\\overline{E B} \\parallel \\overline{D C},$ find $x$", "answer": "9.5", "image_path": "train/2052.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "13.7", "image_path": "train/2053.png"}
{"question": "$\\triangle ABC \\cong \\triangle FGH$. Find $x$.", "answer": "3", "image_path": "train/2054.png"}
{"question": "Points $S$, $T$, and $U$ are the midpoints of $\\overline{DE}$, $\\overline{EF}$, and $\\overline{DF}$, respectively. Find $x$.", "answer": "4", "image_path": "train/2055.png"}
{"question": "Find $m \\angle DBA$.", "answer": "17", "image_path": "train/2056.png"}
{"question": "Circle $L$ has a radius of 32 centimeters. $\\overline{L H} \\perp \\overline{G J},$ and $G J=40$ centimeters. Find $L K$", "answer": "\\sqrt { 624 }", "image_path": "train/2057.png"}
{"question": "$\\triangle RST \\cong \\triangle VUT$. What is the area of $\\triangle RST$?", "answer": "300", "image_path": "train/2058.png"}
{"question": "Find x. Assume that any segment that appears to be tangent is tangent.", "answer": "8", "image_path": "train/2059.png"}
{"question": "In the figure, $m∠4 = 104$, $m∠14 = 118$. Find the measure of $\\angle 9$.", "answer": "62", "image_path": "train/2060.png"}
{"question": "Find the area of the parallelogram.", "answer": "318.7", "image_path": "train/2061.png"}
{"question": "Find $m \\angle C$.", "answer": "47", "image_path": "train/2062.png"}
{"question": "Find x", "answer": "4 \\sqrt { 3 }", "image_path": "train/2063.png"}
{"question": "$m∠4 = 32$. Find the measure of $\\angle 3$.", "answer": "90", "image_path": "train/2064.png"}
{"question": "If $\\overline{W P}$ is a perpendicular bisector, $m \\angle WHA=8 q+17$, $m \\angle HWP=10+q$, $AP=6 r+4$, and $PH=22+3 r$, find $r$.", "answer": "6", "image_path": "train/2065.png"}
{"question": "Find x.", "answer": "5 \\sqrt { 3 }", "image_path": "train/2066.png"}
{"question": "Find the measure of $RT$ of equilateral triangle $RST$ if $RS = x + 9$, $ST = 2x$, and $RT = 3x - 9$.", "answer": "18", "image_path": "train/2067.png"}
{"question": "Find $m \\angle 4$.", "answer": "52", "image_path": "train/2068.png"}
{"question": "Find x.", "answer": "10", "image_path": "train/2069.png"}
{"question": "Find the area of $▱EFGH$.", "answer": "90", "image_path": "train/2070.png"}
{"question": "For trapezoid $T R S V, M$ and $N$ are midpoints of the legs. If $V S=21$ and $T R=44,$ find $M N$", "answer": "32.5", "image_path": "train/2071.png"}
{"question": " $m \\widehat{G H}=78$ Find $m\\angle 2$", "answer": "51", "image_path": "train/2072.png"}
{"question": "Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "answer": "6", "image_path": "train/2073.png"}
{"question": "Find $x$.", "answer": "170", "image_path": "train/2074.png"}
{"question": "For the pair of similar figures, find the area of the green figure.", "answer": "24", "image_path": "train/2075.png"}
{"question": "Find x.", "answer": "5 \\sqrt { 2 }", "image_path": "train/2076.png"}
{"question": "Find the area of the quadrilateral.", "answer": "240", "image_path": "train/2077.png"}
{"question": "Find y.", "answer": "10", "image_path": "train/2078.png"}
{"question": "If $\\overline{GH} \\cong \\overline{HK}$, $\\overline{HJ} \\cong \\overline{YK}$, and $m \\angle GJK=100$, what is the measure of $\\angle HGK$ ?", "answer": "20", "image_path": "train/2079.png"}
{"question": "$ACDF \\sim VWYZ$. Find $x$.", "answer": "15", "image_path": "train/2080.png"}
{"question": "Find the angle measure of $\\angle 2$.", "answer": "128", "image_path": "train/2081.png"}
{"question": "ABCD is a rhombus. If EB = 9, AB = 12 and $m\\angle ABD = 55$ . Find CE", "answer": "\\sqrt { 63 }", "image_path": "train/2082.png"}
{"question": "Find the measure of $\\angle 3$.", "answer": "14", "image_path": "train/2083.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth.", "answer": "46.5", "image_path": "train/2084.png"}
{"question": "$\\overline{PQ}$ is tangent to circles $R$ and $S$. Find $PQ$.", "answer": "4 \\sqrt 6", "image_path": "train/2085.png"}
{"question": "If $SP=4, PT=6$, and $QR=12$, find $SQ$.", "answer": "8", "image_path": "train/2086.png"}
{"question": "If $\\overline{PQ} \\cong \\overline{UQ}$ and $ m ∠ P = 32 $, find $ m ∠PUQ $.", "answer": "32", "image_path": "train/2087.png"}
{"question": "If CDFG is a kite, find GF", "answer": "5", "image_path": "train/2088.png"}
{"question": "Find $\\angle1$", "answer": "112", "image_path": "train/2089.png"}
{"question": "If $x=7 \\sqrt{3},$ find $y$", "answer": "21 \\sqrt { 3 }", "image_path": "train/2090.png"}
{"question": "Find the variable of $r$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "1.8", "image_path": "train/2091.png"}
{"question": "Find $m \\angle DH$.", "answer": "162", "image_path": "train/2092.png"}
{"question": "Find $m \\angle 4$.", "answer": "64", "image_path": "train/2093.png"}
{"question": "Quadrilateral MNOP is a rhombus. If $m\\angle PON = 124$, find $m\\angle POM$.", "answer": "62", "image_path": "train/2094.png"}
{"question": "Find the area of the figure. Round to the nearest tenth.", "answer": "3.5", "image_path": "train/2095.png"}
{"question": "$\\overline{PM}$ is a diameter of $\\odot R$. Find $m \\widehat {MNP}$.", "answer": "180", "image_path": "train/2096.png"}
{"question": "Find x.", "answer": "15.5", "image_path": "train/2097.png"}
{"question": "Find y in the figure.", "answer": "5", "image_path": "train/2098.png"}
{"question": "For the pair of similar figures, use the given areas to find $x$.", "answer": "10.0", "image_path": "train/2099.png"}
{"question": "Circle $A$ has diameters $\\overline{D F}$ and $\\overline{P G}$\r\nIf $P A=7,$ find $P G$", "answer": "14", "image_path": "train/2100.png"}