validation.jsonl

{"question": "Find $x$ so that $m || n$.", "answer": "63", "image_path": "validation/0.png"}
{"question": "Find the value of the variable $x$ in the figure.", "answer": "54", "image_path": "validation/1.png"}
{"question": "Find y. Round to the nearest tenth.", "answer": "33.4", "image_path": "validation/2.png"}
{"question": "Find $m\\angle A$", "answer": "105", "image_path": "validation/3.png"}
{"question": "In $\\odot P$, $JK=10$ and $\\widehat {JKL}=134$. Find $PQ$. Round to the nearest hundredth.", "answer": "3.32", "image_path": "validation/4.png"}
{"question": "Find $x$ in the given parallelogram", "answer": "31", "image_path": "validation/5.png"}
{"question": "Find x.", "answer": "38.1", "image_path": "validation/6.png"}
{"question": "Find the measure of $\\angle B$. Round to the nearest degree.", "answer": "50", "image_path": "validation/7.png"}
{"question": "Find $AC$.", "answer": "14", "image_path": "validation/8.png"}
{"question": "In $\\odot S, m \\angle T S R=42$\r\nFind $m\\widehat{ERT}$", "answer": "180", "image_path": "validation/9.png"}
{"question": "Find $m \\widehat {GH}$.", "answer": "140", "image_path": "validation/10.png"}
{"question": "In $\\odot P$, $RT=15$, find $m \\widehat {RS}$. Round to the nearest hundredth.", "answer": "17.02", "image_path": "validation/11.png"}
{"question": "$Find m \\angle 1$", "answer": "138", "image_path": "validation/12.png"}
{"question": "Find the perimeter of $\\triangle A D F,$ if $\\triangle A D F \\sim \\triangle B C E, B C=24$, $E B=12, C E=18,$ and $D F=21$.", "answer": "63", "image_path": "validation/13.png"}
{"question": "In the figure, $m ∠ 12 = 64$. Find the measure of $ \\angle 9$.", "answer": "116", "image_path": "validation/14.png"}
{"question": "In the figure, $m \\angle 3 = 133$. Find $m\\angle5$.", "answer": "133", "image_path": "validation/15.png"}
{"question": "Find $x$.", "answer": "152", "image_path": "validation/16.png"}
{"question": "Find $m \\angle 1$.", "answer": "110", "image_path": "validation/17.png"}
{"question": "Find x.", "answer": "18", "image_path": "validation/18.png"}
{"question": "Find $m \\angle 4$.", "answer": "56", "image_path": "validation/19.png"}
{"question": "Circles $G, J,$ and $K$ all intersect at $L$ If $G H=10,$ Find FG.", "answer": "10", "image_path": "validation/20.png"}
{"question": "Find x", "answer": "\\frac { 40 } { 3 }", "image_path": "validation/21.png"}
{"question": "Find $x$. A = 165 cm$^2$.", "answer": "11", "image_path": "validation/22.png"}
{"question": "In rhombus $A B C D, m \\angle D A B=2, m \\angle A D C$ and $C B=6$ Find $m \\angle D A B$", "answer": "120", "image_path": "validation/23.png"}
{"question": "Find $m\\widehat{ES}$", "answer": "100", "image_path": "validation/24.png"}
{"question": "The diameters of $\\odot A, \\odot B,$ and $\\odot C$ are 10 inches,\r\n20 inches, and 14 inches, respectively.\r\nFind XB", "answer": "5", "image_path": "validation/25.png"}
{"question": "Find the value of $x$", "answer": "71", "image_path": "validation/26.png"}
{"question": "Find the measure of $\\angle A$", "answer": "158", "image_path": "validation/27.png"}
{"question": "In $\\odot P, P R=15$ and $m \\angle Q P R=120 .$ Find the length of $\\widehat{Q R}$", "answer": "10 \\pi", "image_path": "validation/28.png"}
{"question": "$\\overline{AD}$ and $\\overline{CG}$ are diameters of $\\odot B$. Find $m \\widehat {AC}$.", "answer": "125", "image_path": "validation/29.png"}
{"question": "Find the value of the variable $x$ in the figure.", "answer": "60", "image_path": "validation/30.png"}
{"question": "Find $JL$.", "answer": "24", "image_path": "validation/31.png"}
{"question": "In $\\odot C$, $m \\angle HCG=2x$ and $m \\angle HCD=6x+28$, find $m \\widehat {HGF}$.", "answer": "128", "image_path": "validation/32.png"}
{"question": "In $\\odot G, m \\angle A G B=30$ and $\\overline{C G} \\perp \\overline{G D}$.\r\nFind $m \\widehat{F A B}$", "answer": "180", "image_path": "validation/33.png"}
{"question": "Find the measure of $∠Z$ to the nearest tenth.", "answer": "44.4", "image_path": "validation/34.png"}
{"question": "If $\\sin x=0.6$ and $A B=12,$ what is the area of $\\triangle A B C ?$", "answer": "34.6", "image_path": "validation/35.png"}
{"question": "Find $DE$ if $AB=6, AF=8, BC=x, CD=y$, $DE=2y-3,$ and $FE=x+\\frac{10}{3}$.", "answer": "15", "image_path": "validation/36.png"}
{"question": "Find $m \\angle A$.", "answer": "81", "image_path": "validation/37.png"}
{"question": "What is the perimeter of the right triangle below? Round your answer to the nearest tenth if necessary.", "answer": "33.5", "image_path": "validation/38.png"}
{"question": "In $\\odot F, m \\angle D F A=50$ and $\\overline{C F} \\perp \\overline{F B}$. Find $m \\widehat{B E}$", "answer": "50", "image_path": "validation/39.png"}
{"question": "Find x.", "answer": "12", "image_path": "validation/40.png"}
{"question": "In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\\angle 3$.", "answer": "62", "image_path": "validation/41.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 $\\angle DGF$. ", "answer": "124", "image_path": "validation/42.png"}
{"question": "Find $x$.", "answer": "4.5", "image_path": "validation/43.png"}
{"question": "Find $x$.", "answer": "10", "image_path": "validation/44.png"}
{"question": "In $\\odot E$, $EG = EF$. Find $AB$.", "answer": "27", "image_path": "validation/45.png"}
{"question": "Find the perimeter of the triangle. Round to the nearest hundredth.", "answer": "13.84", "image_path": "validation/46.png"}
{"question": "Find $m\\angle 2$.", "answer": "80", "image_path": "validation/47.png"}
{"question": "Find $b$ in the given parallelogram", "answer": "4", "image_path": "validation/48.png"}
{"question": "Find x", "answer": "16 \\sqrt { 3 }", "image_path": "validation/49.png"}
{"question": "Find the perimeter of ABCD", "answer": "24 + 4 \\sqrt { 2 } + 4 \\sqrt { 3 }", "image_path": "validation/50.png"}
{"question": "In $\\odot F$, if $CF=14$ inches, what is the diameter of the circle?", "answer": "28", "image_path": "validation/51.png"}
{"question": "Find $x$ so that $m || n$.", "answer": "22", "image_path": "validation/52.png"}
{"question": "For the pair of similar figures, use the given areas to find $x$.", "answer": "36", "image_path": "validation/53.png"}
{"question": "If $m \\angle CFD=12 a+45$, find $a$ so that $\\overrightarrow {FC} \\perp \\overrightarrow{FD}$.", "answer": "3.75", "image_path": "validation/54.png"}
{"question": "Find the measure of $\\angle 1$ in the figure.", "answer": "128", "image_path": "validation/55.png"}
{"question": "Find the measure of $∠T$ to the nearest tenth.", "answer": "61.4", "image_path": "validation/56.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "50", "image_path": "validation/57.png"}
{"question": "What is $m∠1$ in the figure below?", "answer": "85", "image_path": "validation/58.png"}
{"question": "Find $m \\angle 2$.", "answer": "37.5", "image_path": "validation/59.png"}
{"question": "Quadrilateral WXYZ is a rectangle.  If $PY = 3x - 5$ and $WP = 2x + 11$, find $ZP$.", "answer": "43", "image_path": "validation/60.png"}
{"question": "In the figure, $ \\triangle ABC$ is isosceles, $ \\triangle DCE$ is equilateral, and $ \\triangle FCG$ is isosceles. Find the measures of the $\\angle 1$ at vertex $C$.\r\n", "answer": "18", "image_path": "validation/61.png"}
{"question": "Find b", "answer": "4.6", "image_path": "validation/62.png"}
{"question": "Find the value of x in the figure at the right.", "answer": "5.42", "image_path": "validation/63.png"}
{"question": "Find z.", "answer": "10 \\sqrt { 2 }", "image_path": "validation/64.png"}
{"question": "If the circumference of the circle is $16 \\pi$ units, what is the total area of the shaded regions?", "answer": "32 \\pi", "image_path": "validation/65.png"}
{"question": "If $A B=32$ and $F C=11,$ find $F E$", "answer": "\\sqrt { 135 }", "image_path": "validation/66.png"}
{"question": "Find y", "answer": "45", "image_path": "validation/67.png"}
{"question": "$Q$ is the incenter of $\\triangle JKL$. Find $QP$.", "answer": "15", "image_path": "validation/68.png"}
{"question": "The common chord $\\overline{AB}$ between $\\odot P$ and $\\odot Q$ is perpendicular to the segment connecting the centers of the circles. If $AB=10$ what is the length of $\\overline{PQ}$?", "answer": "4 \\sqrt 6 + 2 \\sqrt { 14 }", "image_path": "validation/69.png"}
{"question": "If $BEFA \\sim EDCB$, find $x$.", "answer": "4", "image_path": "validation/70.png"}
{"question": "Find $m \\angle T$.", "answer": "60", "image_path": "validation/71.png"}
{"question": "$WXYZ$ is a rhombus. If $m \\angle XYZ=110$, find $m \\angle ZWY$.", "answer": "55", "image_path": "validation/72.png"}
{"question": "If PR || WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find PY", "answer": "5", "image_path": "validation/73.png"}
{"question": "Find AB", "answer": "15", "image_path": "validation/74.png"}
{"question": "Find $x$.", "answer": "225", "image_path": "validation/75.png"}
{"question": "In circle $F$, what is the measure of $\\widehat{E A}$ if $m \\angle D F E \\text { is } 36 ? $", "answer": "144", "image_path": "validation/76.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram", "answer": "7", "image_path": "validation/77.png"}
{"question": "Find $x$.", "answer": "144", "image_path": "validation/78.png"}
{"question": "Find the measure of $\\angle 5$.", "answer": "75", "image_path": "validation/79.png"}
{"question": "If the perimeter of square 2 is 200 units and the perimeter of square 1 is 150 units, what is the perimeter of square 3?", "answer": "250", "image_path": "validation/80.png"}
{"question": "Find $x$ so that each quadrilateral is a parallelogram.", "answer": "1", "image_path": "validation/81.png"}
{"question": "Find z.", "answer": "8 \\sqrt { 5 }", "image_path": "validation/82.png"}
{"question": "Find y", "answer": "6.4", "image_path": "validation/83.png"}
{"question": "Find the length of $\\widehat {BC}$.", "answer": "2.20", "image_path": "validation/84.png"}
{"question": "Use parallelogram JKLM to find $m \\angle MJK$ if $J K=2 b+3$ and $J M=3 a$.", "answer": "100", "image_path": "validation/85.png"}
{"question": "Find the area of the figure.", "answer": "96", "image_path": "validation/86.png"}
{"question": "Find $RS$.", "answer": "9", "image_path": "validation/87.png"}
{"question": "For the pair of similar figures, use the given areas to find $x$.", "answer": "17.5", "image_path": "validation/88.png"}
{"question": "Which polynomial best represents the area of the regular pentagon shown below?", "answer": "20 y^2 - 10 y", "image_path": "validation/89.png"}
{"question": "If $\\overline{NQ}$ and $\\overline{VX}$ are medians, $\\triangle PNR \\sim \\triangle WVY, NQ=8, PR=12,WY=7x-1,$ and $VX=4x+2,$ find $x$.", "answer": "4", "image_path": "validation/90.png"}
{"question": "Find the perimeter of the $\\triangle WZX$, if $\\triangle WZX \\sim \\triangle SRT$, $ST=6, WX=5$, and the perimeter of $\\triangle SRT=15$.", "answer": "12.5", "image_path": "validation/91.png"}
{"question": "ABCD is a rectangle.  If $C F=4 x+1$ and $D F=x+13,$ find $x$", "answer": "4", "image_path": "validation/92.png"}
{"question": "If $\\overline{PR} \\| \\overline{WX}, WX=10, XY=6, WY=8, RY=5,$ and $PS=3,$ find $PY$.", "answer": "5", "image_path": "validation/93.png"}
{"question": "Find $m \\widehat{A C}$", "answer": "58", "image_path": "validation/94.png"}
{"question": "What is the area of the parallelogram below? Round to the nearest whole number if necessary.", "answer": "106.0", "image_path": "validation/95.png"}
{"question": "Find $AF$.", "answer": "11", "image_path": "validation/96.png"}
{"question": "Find $m \\angle 1$.", "answer": "42", "image_path": "validation/97.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": "26.6", "image_path": "validation/98.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 $m\\angle LQP$", "answer": "140", "image_path": "validation/99.png"}
{"question": "Find $x$ so that each quadrilateral is a parallelogram.", "answer": "41", "image_path": "validation/100.png"}
{"question": "If $A B=8, K L=10,$ and $J B=13,$ find $J L$", "answer": "16.25", "image_path": "validation/101.png"}
{"question": "Find y.", "answer": "8 \\sqrt { 3 }", "image_path": "validation/102.png"}
{"question": "Find $y$ so that each quadrilateral is a parallelogram.", "answer": "2", "image_path": "validation/103.png"}
{"question": "Quadrilateral $ABCD$ is a rhombus. If $DB = 2x – 4$ and $PB = 2x – 9$, find $PD$.", "answer": "5", "image_path": "validation/104.png"}
{"question": "If $\\overrightarrow{AC}$ bisects $\\angle DAB, BC=4x+8,$ and $DC=9x-7$, find $BC$.", "answer": "20", "image_path": "validation/105.png"}
{"question": "Find the length of $\\widehat {AB}$. Round to the nearest hundredth.", "answer": "16.76", "image_path": "validation/106.png"}
{"question": "Find the measure of $\\angle 5$ if $\\overline{A B} \\perp \\overline{B C}$.", "answer": "64", "image_path": "validation/107.png"}
{"question": "Find the perimeter of parallelogram ABCD to the nearest tenth.", "answer": "34.6", "image_path": "validation/108.png"}
{"question": "Find the circumference of the figure. Round to the nearest tenth.", "answer": "36.4", "image_path": "validation/109.png"}
{"question": "Find $x$ so that $p \\parallel q$.", "answer": "15", "image_path": "validation/110.png"}
{"question": "$P$ is the incenter of $\\triangle AEC$. Find $PB$. Rounded to the nearest hundredth.", "answer": "7.08", "image_path": "validation/111.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth.", "answer": "69.5", "image_path": "validation/112.png"}
{"question": "Find the perimeter of quadrilateral ABCD to the nearest tenth.", "answer": "56.9", "image_path": "validation/113.png"}
{"question": "Which statement about the value of $x$ is not true?", "answer": "x < 60", "image_path": "validation/114.png"}
{"question": "In the figure, $m∠4 = 101$. Find the measure of $\\angle 7$.", "answer": "79", "image_path": "validation/115.png"}
{"question": "Find $m \\angle 1$.", "answer": "38", "image_path": "validation/116.png"}
{"question": "Point $S$ is the incenter of $\\triangle JPL$. Find $QJ$.", "answer": "8", "image_path": "validation/117.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 $x$", "answer": "2", "image_path": "validation/118.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "96.5", "image_path": "validation/119.png"}
{"question": "Find x", "answer": "2", "image_path": "validation/120.png"}
{"question": "Find y.", "answer": "18", "image_path": "validation/121.png"}
{"question": "Find the variable of $a$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "15.0", "image_path": "validation/122.png"}
{"question": "Find $m \\widehat{B C}$", "answer": "123", "image_path": "validation/123.png"}
{"question": "Find $m \\angle 2$.", "answer": "21", "image_path": "validation/124.png"}
{"question": "Find $G K$ if $G I=14, G H=7,$ and $K J=6$", "answer": "6", "image_path": "validation/125.png"}
{"question": "Find the value of $x$.", "answer": "58", "image_path": "validation/126.png"}
{"question": "Find AP", "answer": "8 \\sqrt { 3 }", "image_path": "validation/127.png"}
{"question": "Find $m \\angle R C N$", "answer": "103", "image_path": "validation/128.png"}
{"question": "Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "answer": "3.2", "image_path": "validation/129.png"}
{"question": "If $m \\widehat{A E}=75,$ find $m \\angle A D E$", "answer": "37.5", "image_path": "validation/130.png"}
{"question": "Find y", "answer": "29.2", "image_path": "validation/131.png"}
{"question": "Find $m \\angle R$.", "answer": "62", "image_path": "validation/132.png"}
{"question": "Find x. Round to the nearest tenth if necessary.", "answer": "28.1", "image_path": "validation/133.png"}
{"question": "Find y.", "answer": "\\frac { 17 } { 2 }", "image_path": "validation/134.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "814", "image_path": "validation/135.png"}
{"question": "RS is the midsegment of trapezoid MNOP. What is the length of RS ?", "answer": "26", "image_path": "validation/136.png"}
{"question": "Find $m\\angle D$", "answer": "134", "image_path": "validation/137.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 $\\angle Y$", "answer": "108", "image_path": "validation/138.png"}
{"question": "Refer to the figure at the right. Find the value of $m ∠ CBD $ if $ p \\parallel q $.", "answer": "105", "image_path": "validation/139.png"}
{"question": "Find $m \\angle 3$.", "answer": "82", "image_path": "validation/140.png"}
{"question": "find $tanS$", "answer": "0.75", "image_path": "validation/141.png"}
{"question": "Use parallelogram to  find $y$", "answer": "101", "image_path": "validation/142.png"}
{"question": "Find x", "answer": "\\frac { 40 } { 3 }", "image_path": "validation/143.png"}
{"question": "Express the ratio of $\\sin V$ as a decimal to the nearest hundredth.", "answer": "0.28", "image_path": "validation/144.png"}
{"question": "Find $m\\angle Y X W$", "answer": "115", "image_path": "validation/145.png"}
{"question": "Find $x$.", "answer": "17.5", "image_path": "validation/146.png"}
{"question": "In the figure, $m∠4 = 104$, $m∠14 = 118$. Find the measure of $\\angle 2$.", "answer": "104", "image_path": "validation/147.png"}
{"question": "In $\\triangle D E F, P$ is the midpoint of $\\overline{D E},$ and $Q$ is the midpoint of side $\\overline{D F} .$ If $E F=3 x+4$ and $P Q=20$, what is the value of $x ?", "answer": "12", "image_path": "validation/148.png"}
{"question": "Find $QS$ if $\\triangle QRS$ is an equilateral triangle.", "answer": "2", "image_path": "validation/149.png"}
{"question": "WXYZ is a square. If $WT = 3$, Find $m \\angle WYX$", "answer": "45", "image_path": "validation/150.png"}
{"question": "Find x. Round to the nearest tenth.", "answer": "6.2", "image_path": "validation/151.png"}
{"question": "Find the base of the parallelogram given its area with 2000 square units.", "answer": "50", "image_path": "validation/152.png"}
{"question": "In the figure, $m∠8 = 96$ and $m∠12 = 42$. Find the measure of $\\angle 11$.", "answer": "138", "image_path": "validation/153.png"}
{"question": "Find y.", "answer": "7 \\sqrt { 3 }", "image_path": "validation/154.png"}
{"question": "Find the measure of $\\angle Q$", "answer": "106", "image_path": "validation/155.png"}
{"question": "Find $x$.", "answer": "8", "image_path": "validation/156.png"}
{"question": "If $m \\angle B N C=20,$ find $m \\widehat{B C}$", "answer": "20", "image_path": "validation/157.png"}
{"question": "If $m \\angle F=7x+2$ and $m \\angle H=17x-8$, find $x$.", "answer": "4", "image_path": "validation/158.png"}
{"question": "Find $DH$.", "answer": "20", "image_path": "validation/159.png"}
{"question": "The pair of polygons is similar. Find AG", "answer": "13.5", "image_path": "validation/160.png"}
{"question": "Find x. Assume that any segment that appears to be tangent is tangent.", "answer": "30", "image_path": "validation/161.png"}
{"question": "Find the measure of $\\angle 4$ if $m∠DGF = 53$ and $m∠AGC = 40$.", "answer": "40", "image_path": "validation/162.png"}
{"question": "Find $m \\angle 1$.", "answer": "61", "image_path": "validation/163.png"}
{"question": "Use parallelogram PQRS to find $m\\angle S$", "answer": "128", "image_path": "validation/164.png"}
{"question": "Find z.", "answer": "32", "image_path": "validation/165.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 $m \\angle PXR=2 a+10$.  If $\\widetilde{Q Y}$ is a perpendicular bisector of $\\overline{P R}$, find $b$.", "answer": "12", "image_path": "validation/166.png"}
{"question": "Circle $W$ has a radius of 4 units, $\\odot Z$ has a radius of 7 units, and $X Y=2 .$ Find $I X$", "answer": "6", "image_path": "validation/167.png"}
{"question": "Find $x$.", "answer": "16", "image_path": "validation/168.png"}
{"question": "For isosceles trapezoid $X Y Z W$ find $m \\angle W$", "answer": "110", "image_path": "validation/169.png"}
{"question": "Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "96", "image_path": "validation/170.png"}
{"question": "Use parallelogram to find $x$", "answer": "58", "image_path": "validation/171.png"}
{"question": "Find the value of x.", "answer": "3", "image_path": "validation/172.png"}
{"question": "Find the area of the shaded region. Assume the inscribed polygon is regular.", "answer": "39.3", "image_path": "validation/173.png"}
{"question": "Find y.", "answer": "\\frac { 325 } { 6 }", "image_path": "validation/174.png"}
{"question": "ABCD is a rectangle.  If $m \\angle 1=12 x+4$ and $m \\angle 2=16 x-12,$ find $m \\angle 2$", "answer": "52", "image_path": "validation/175.png"}
{"question": "Find $y$.", "answer": "3", "image_path": "validation/176.png"}
{"question": "The segment is tangent to the circle. Find $x$.", "answer": "26", "image_path": "validation/177.png"}
{"question": "Find $y$ so that the quadrilateral is a parallelogram.", "answer": "8", "image_path": "validation/178.png"}
{"question": "Find $m \\widehat {JM}$.", "answer": "155", "image_path": "validation/179.png"}
{"question": "Find the area of the kite.", "answer": "84", "image_path": "validation/180.png"}
{"question": "Find $x$ in the figure.", "answer": "3", "image_path": "validation/181.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "71.8", "image_path": "validation/182.png"}
{"question": "If $WX=7$, $WY=a$, $WV=6$, and $VZ=a-9$, find $WY$.", "answer": "21", "image_path": "validation/183.png"}
{"question": "Find $y$.", "answer": "4", "image_path": "validation/184.png"}
{"question": "Find $m∠B$.", "answer": "76", "image_path": "validation/185.png"}
{"question": "Find y.", "answer": "10 \\sqrt { 3 }", "image_path": "validation/186.png"}
{"question": "Find $m \\angle 3$.", "answer": "63", "image_path": "validation/187.png"}
{"question": "Find x.", "answer": "16.8", "image_path": "validation/188.png"}
{"question": "In $\\odot P, P D=10, P Q=10,$ and $Q E=20$, find AB", "answer": "40", "image_path": "validation/189.png"}
{"question": "Find z.", "answer": "2 \\sqrt { 13 }", "image_path": "validation/190.png"}
{"question": "Find DE", "answer": "4", "image_path": "validation/191.png"}
{"question": "$UJ=9, VJ=3$, and $ZT=18$. Find $YU$.", "answer": "13.5", "image_path": "validation/192.png"}
{"question": "Find x.", "answer": "42", "image_path": "validation/193.png"}
{"question": "$\\overline{A B}, \\overline{B C}, \\overline{C D},$ and $\\overline{A D}$ are tangent to a circle. If $A B=19, B C=6,$ and $C D=14,$ find $A D$", "answer": "27", "image_path": "validation/194.png"}
{"question": "Express the ratio of $\\cos A$ as a decimal to the nearest hundredth.", "answer": "0.92", "image_path": "validation/195.png"}
{"question": "Find y. Round to the nearest tenth, if necessary.", "answer": "4", "image_path": "validation/196.png"}
{"question": "Find y", "answer": "4 \\sqrt { 2 }", "image_path": "validation/197.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "612.5", "image_path": "validation/198.png"}
{"question": "In the figure, $m ∠9 = 75$. Find the measure of $\\angle 11$.", "answer": "75", "image_path": "validation/199.png"}
{"question": "Find y", "answer": "3 \\sqrt { 2 }", "image_path": "validation/200.png"}
{"question": "Find y.", "answer": "3 \\sqrt { 13 }", "image_path": "validation/201.png"}
{"question": "Find y", "answer": "9 \\sqrt { 3 }", "image_path": "validation/202.png"}
{"question": "Find the value of the variable $y$ in the figure.", "answer": "114", "image_path": "validation/203.png"}
{"question": "Find x.", "answer": "9", "image_path": "validation/204.png"}
{"question": "If $b=3,$ find $a$", "answer": "\\sqrt { 3 }", "image_path": "validation/205.png"}
{"question": "Find y.", "answer": "16", "image_path": "validation/206.png"}
{"question": "$a=8, b=15,$ and $c=17$ find $sinB$", "answer": "0.88", "image_path": "validation/207.png"}
{"question": "$\\Delta EFG$ is equilateral, and $\\overline{E H}$ bisects $\\angle E$. Find $m \\angle 1$.", "answer": "30", "image_path": "validation/208.png"}
{"question": "In the figure, $m ∠1 = 53$. Find the measure of $∠7$.", "answer": "127", "image_path": "validation/209.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 ratio of the perimeter of polygon ABCD to the perimeter of polygon AEFG", "answer": "1.6", "image_path": "validation/210.png"}
{"question": "Find $m \\angle BAC$.", "answer": "60", "image_path": "validation/211.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "6", "image_path": "validation/212.png"}
{"question": "Find the area of the shaded sector. Round to the nearest tenth.", "answer": "175.8", "image_path": "validation/213.png"}
{"question": "Suppose $∠4$ and $∠5$ form a linear pair. If $m∠1 = 2x$, $m∠2 = 3x - 20$, and $m∠3 = x - 4$, what is $m∠3$?", "answer": "30", "image_path": "validation/214.png"}
{"question": "Point $S$ is the incenter of $\\triangle JPL$. Find $SQ$.", "answer": "6", "image_path": "validation/215.png"}
{"question": "Find x", "answer": "6", "image_path": "validation/216.png"}
{"question": "$\\triangle LMN \\cong \\triangle QRS$. Find $y$.", "answer": "18", "image_path": "validation/217.png"}
{"question": "Find $x$. Assume that segments that appear to be tangent are tangent.", "answer": "32", "image_path": "validation/218.png"}
{"question": "$\\overline{TV}$ is tangent to the circle, and R and S are points on the circle. What is the value of x to the nearest tenth?", "answer": "5.7", "image_path": "validation/219.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 $m\\angle PQS$", "answer": "63.5", "image_path": "validation/220.png"}
{"question": "In the figure, $m∠1 = 94$. Find the measure of $\\angle 4$.", "answer": "86", "image_path": "validation/221.png"}
{"question": "Find the measure of the altitude drawn to the hypotenuse.", "answer": "3 \\sqrt { 5 }", "image_path": "validation/222.png"}
{"question": "Find the area of the regular polygon. Round to the nearest tenth.", "answer": "6.9", "image_path": "validation/223.png"}
{"question": "Find x.", "answer": "\\sqrt { 218 }", "image_path": "validation/224.png"}
{"question": "Find the area of the shaded region. Round to the nearest tenth if necessary.", "answer": "202", "image_path": "validation/225.png"}
{"question": "In the figure, $m ∠1 = 58 $, $m ∠2 = 47 $, and $m ∠3 = 26 $. Find the measure of $∠6$.", "answer": "75", "image_path": "validation/226.png"}
{"question": "Find $JK$.", "answer": "8", "image_path": "validation/227.png"}
{"question": "Find $x$ if $\\triangle QRS$ is an equilateral triangle.", "answer": "0.5", "image_path": "validation/228.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "12.4", "image_path": "validation/229.png"}
{"question": "Find $m \\angle 8$.", "answer": "65", "image_path": "validation/230.png"}
{"question": "If $\\overline{RQ} \\cong \\overline{RS}$, $\\overline{RP} \\cong \\overline{RT}$ and $ m ∠RQS = 80 $, find $ m ∠P $.", "answer": "80", "image_path": "validation/231.png"}
{"question": "Find the value of the variable m.", "answer": "4", "image_path": "validation/232.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "165", "image_path": "validation/233.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 $m\\widehat{W U Y}$", "answer": "256", "image_path": "validation/234.png"}
{"question": "In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\\angle 5$.", "answer": "80", "image_path": "validation/235.png"}
{"question": "Find y", "answer": "21", "image_path": "validation/236.png"}
{"question": "Find $WY$.", "answer": "3", "image_path": "validation/237.png"}
{"question": "Use a Pythagorean Triple to find x.", "answer": "28", "image_path": "validation/238.png"}
{"question": "Find $m \\angle C G B$", "answer": "120", "image_path": "validation/239.png"}
{"question": "Find $LM$.", "answer": "12", "image_path": "validation/240.png"}
{"question": "Find $E G$ if $\\triangle A C B \\sim \\triangle E G F, \\overline{A D}$ is an altitude of $\\triangle A C B, \\overline{E H}$ is an altitude of $\\triangle E G F, A C=17$, $A D=15,$ and $E H=7.5$", "answer": "8.5", "image_path": "validation/241.png"}
{"question": "Find x. Round side measures to the nearest tenth.", "answer": "19.3", "image_path": "validation/242.png"}
{"question": "Find the perimeter of the triangle. Round to the nearest tenth if necessary.", "answer": "69.9", "image_path": "validation/243.png"}
{"question": "Find the area of the figure. Round to the nearest tenth, if necessary.", "answer": "82.9", "image_path": "validation/244.png"}
{"question": "Find $m \\angle 7$.", "answer": "57", "image_path": "validation/245.png"}
{"question": "Find x. Assume that segments that appear to be tangent are tangent.", "answer": "15", "image_path": "validation/246.png"}
{"question": "Find $PN$.", "answer": "11", "image_path": "validation/247.png"}
{"question": "Find $x$.", "answer": "3", "image_path": "validation/248.png"}
{"question": "Find x", "answer": "53.2", "image_path": "validation/249.png"}
{"question": "Find the value of $x$.", "answer": "55", "image_path": "validation/250.png"}
{"question": "Find $x$.", "answer": "4", "image_path": "validation/251.png"}
{"question": "Find $TY$.", "answer": "7.5", "image_path": "validation/252.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 $m \\angle H M G=4 z+14$. $\\overline{G P}$ is a median of $\\triangle G H J$ . Find $H J$.", "answer": "88", "image_path": "validation/253.png"}
{"question": "QRST is a rectangle. If $m \\angle Q T R=2 x^{2}-7$ and $m \\angle S R T=x^{2}+18,$ find $m \\angle Q T R$", "answer": "43", "image_path": "validation/254.png"}
{"question": "If $J A=25, A K=10,$ and $B L=14,$ find $J B$", "answer": "35", "image_path": "validation/255.png"}
{"question": "Use parallelogram $ABCD$ to find $m \\angle BCD$", "answer": "115", "image_path": "validation/256.png"}
{"question": "Find the perimeter of the figure. Round to the nearest hundredth, if necessary.", "answer": "8", "image_path": "validation/257.png"}
{"question": "Find x. Round the side measure to the nearest tenth.", "answer": "3.8", "image_path": "validation/258.png"}
{"question": "Find x", "answer": "13.6", "image_path": "validation/259.png"}
{"question": "Find $x$ so that $ m \\parallel n $.", "answer": "11.375", "image_path": "validation/260.png"}
{"question": "If $a=4,$ find $c$", "answer": "8", "image_path": "validation/261.png"}
{"question": "Find the value of x. Round to the nearest tenth.", "answer": "7.8", "image_path": "validation/262.png"}
{"question": "Find $x$.", "answer": "20", "image_path": "validation/263.png"}
{"question": "Find z.", "answer": "20", "image_path": "validation/264.png"}
{"question": "In $\\odot S$, $LM=16$ and $PN=4x$. What is $x$?", "answer": "4", "image_path": "validation/265.png"}
{"question": "Find $x$.", "answer": "30", "image_path": "validation/266.png"}
{"question": "In $\\odot P$, $PQ=3$, find $m \\widehat {RTS}$. Round to the nearest hundredth.", "answer": "12.04", "image_path": "validation/267.png"}
{"question": "$a=8, b=15,$ and $c=17$ find $cosA$", "answer": "0.88", "image_path": "validation/268.png"}
{"question": "Find the area of the regular polygon. Round to the nearest tenth.", "answer": "55.4", "image_path": "validation/269.png"}
{"question": "Find $m \\angle 3$.", "answer": "65", "image_path": "validation/270.png"}
{"question": "Find x", "answer": "3.6", "image_path": "validation/271.png"}
{"question": "Find the area of the regular polygon. Round to the nearest tenth.", "answer": "162", "image_path": "validation/272.png"}
{"question": "Which of the following angle pairs are alternate exterior angles?", "answer": "\\angle 2 and \\angle 6", "image_path": "validation/273.png"}
{"question": "Find $y$.", "answer": "3", "image_path": "validation/274.png"}
{"question": "Find y", "answer": "5.5 \\sqrt { 3 }", "image_path": "validation/275.png"}
{"question": "Find x.", "answer": "5 \\sqrt { 13 }", "image_path": "validation/276.png"}
{"question": "Find x.", "answer": "26", "image_path": "validation/277.png"}
{"question": "Find $m∠D$.", "answer": "104", "image_path": "validation/278.png"}
{"question": "What is the value of $x$ below to the nearest tenth?", "answer": "9.7", "image_path": "validation/279.png"}
{"question": "The radius of $\\odot P$ is 5 and $P R=3$. Find QR", "answer": "4", "image_path": "validation/280.png"}
{"question": "Find $y$.", "answer": "- 1", "image_path": "validation/281.png"}
{"question": "Find the perimeter of the figure. Round to the nearest tenth if necessary.", "answer": "92.5", "image_path": "validation/282.png"}
{"question": "Trapezoid $PQRS$ has an area of 250 square inches. Find the height of $PQRS$.", "answer": "10", "image_path": "validation/283.png"}
{"question": "$ \\triangle WXY $  and $ \\triangle XYZ $ are isosceles and $m∠XYZ = 128$. Find the measure of $∠XWY$.", "answer": "52", "image_path": "validation/284.png"}
{"question": "In $\\odot S, m \\angle T S R=42$\r\nFind $m\\widehat{KRT}$", "answer": "222", "image_path": "validation/285.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 $m\\widehat{X Y}$", "answer": "52", "image_path": "validation/286.png"}
{"question": "Find $m \\angle C$.", "answer": "51.75", "image_path": "validation/287.png"}
{"question": "Find the area of the rhombus.", "answer": "90", "image_path": "validation/288.png"}
{"question": "Find the measure of $\\angle2$.", "answer": "70", "image_path": "validation/289.png"}
{"question": "Find $x$ so that each quadrilateral is a parallelogram.", "answer": "14", "image_path": "validation/290.png"}
{"question": "Find the measure of $\\angle 1$.", "answer": "76", "image_path": "validation/291.png"}
{"question": "Find $m \\angle 3$.", "answer": "82", "image_path": "validation/292.png"}
{"question": "In $\\odot H$, $PQ=3x-4$ and $RS=14$. Find $x$.", "answer": "6", "image_path": "validation/293.png"}
{"question": "Find the area of the figure. Round to the nearest tenth if necessary.", "answer": "21", "image_path": "validation/294.png"}
{"question": "Find the measure of $\\angle AFD$ on $\\odot F$ with diameter $\\overline{AC} $.", "answer": "57", "image_path": "validation/295.png"}
{"question": "Find $RT$.", "answer": "13", "image_path": "validation/296.png"}
{"question": "Find $h$.", "answer": "\\frac { 21 \\sqrt 2 } { 2 }", "image_path": "validation/297.png"}
{"question": "Find the measure of $\\angle 1$.", "answer": "60", "image_path": "validation/298.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 $\\angle FGH$. ", "answer": "56", "image_path": "validation/299.png"}