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<image>Find x.
3
[ { "content": "<image>Find x.", "role": "user" }, { "content": "3", "role": "assistant" } ]
<image>If $\overline{B E} \cong \overline{E D}$ and $m \widehat{E D}=120,$ find $m \widehat{B E}$
120
[ { "content": "<image>If $\\overline{B E} \\cong \\overline{E D}$ and $m \\widehat{E D}=120,$ find $m \\widehat{B E}$", "role": "user" }, { "content": "120", "role": "assistant" } ]
<image>Find x.
2 \sqrt { 221 }
[ { "content": "<image>Find x.", "role": "user" }, { "content": "2 \\sqrt { 221 }", "role": "assistant" } ]
<image>Find $x$ so that $m || n$.
27
[ { "content": "<image>Find $x$ so that $m || n$.", "role": "user" }, { "content": "27", "role": "assistant" } ]
<image>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 $\overline{A C}$
27
[ { "content": "<image>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 $\\overline{A C}$", "role": "user" }, { "content": "27", "role"...
<image>Find $m \angle 2$.
34
[ { "content": "<image>Find $m \\angle 2$.", "role": "user" }, { "content": "34", "role": "assistant" } ]
<image>Find the area of a regular hexagon with a perimeter of 72 feet.
374.1
[ { "content": "<image>Find the area of a regular hexagon with a perimeter of 72 feet.", "role": "user" }, { "content": "374.1", "role": "assistant" } ]
<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.
420
[ { "content": "<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.", "role": "user" }, { "content": "420", "role": "assistant" } ]
<image>Find the area of the shaded region. Round to the nearest tenth if necessary.
108.5
[ { "content": "<image>Find the area of the shaded region. Round to the nearest tenth if necessary.", "role": "user" }, { "content": "108.5", "role": "assistant" } ]
<image>The triangle is inscribed into the circle. Find the exact circumference of the circle.
12 \pi
[ { "content": "<image>The triangle is inscribed into the circle. Find the exact circumference of the circle.", "role": "user" }, { "content": "12 \\pi", "role": "assistant" } ]
<image>Find x
4
[ { "content": "<image>Find x", "role": "user" }, { "content": "4", "role": "assistant" } ]
<image>Find the area of the shaded sector. Round to the nearest tenth.
311.5
[ { "content": "<image>Find the area of the shaded sector. Round to the nearest tenth.", "role": "user" }, { "content": "311.5", "role": "assistant" } ]
<image>Find $x$ in the figure.
16
[ { "content": "<image>Find $x$ in the figure.", "role": "user" }, { "content": "16", "role": "assistant" } ]
<image>Find $x$.
35
[ { "content": "<image>Find $x$.", "role": "user" }, { "content": "35", "role": "assistant" } ]
<image>In the figure, square $WXYZ$ is inscribed in $\odot R$. Find the measure of a central angle.
90
[ { "content": "<image>In the figure, square $WXYZ$ is inscribed in $\\odot R$. Find the measure of a central angle.", "role": "user" }, { "content": "90", "role": "assistant" } ]
<image>Find y.
45
[ { "content": "<image>Find y.", "role": "user" }, { "content": "45", "role": "assistant" } ]
<image>Find $\angle D$ of quadrilateral ABCD
45
[ { "content": "<image>Find $\\angle D$ of quadrilateral ABCD", "role": "user" }, { "content": "45", "role": "assistant" } ]
<image>Find $x$.
70
[ { "content": "<image>Find $x$.", "role": "user" }, { "content": "70", "role": "assistant" } ]
<image>The diagonals of rhombus FGHJ intersect at K. If $m\angle FJH = 82$, find $m\angle KHJ$.
49
[ { "content": "<image>The diagonals of rhombus FGHJ intersect at K. \r\nIf $m\\angle FJH = 82$, find $m\\angle KHJ$.", "role": "user" }, { "content": "49", "role": "assistant" } ]
<image>Find $y$ in the given parallelogram
15
[ { "content": "<image>Find $y$ in the given parallelogram", "role": "user" }, { "content": "15", "role": "assistant" } ]
<image>Find $HK$.
10
[ { "content": "<image>Find $HK$.", "role": "user" }, { "content": "10", "role": "assistant" } ]
<image>$\triangle RST \cong \triangle XYZ$. Find $y$.
15
[ { "content": "<image>$\\triangle RST \\cong \\triangle XYZ$. Find $y$.", "role": "user" }, { "content": "15", "role": "assistant" } ]
<image>Find x. Round to the nearest tenth.
24.7
[ { "content": "<image>Find x. Round to the nearest tenth.", "role": "user" }, { "content": "24.7", "role": "assistant" } ]
<image>Find DX if $E X=24$ and $D E=7$
25
[ { "content": "<image>Find DX if $E X=24$ and $D E=7$", "role": "user" }, { "content": "25", "role": "assistant" } ]
<image>Find $TR$.
4
[ { "content": "<image>Find $TR$.", "role": "user" }, { "content": "4", "role": "assistant" } ]
<image>Find z
2 \sqrt { 6 }
[ { "content": "<image>Find z", "role": "user" }, { "content": "2 \\sqrt { 6 }", "role": "assistant" } ]
<image>Find the measure of $\angle 4$ if $m∠4= m∠5$.
32
[ { "content": "<image>Find the measure of $\\angle 4$ if $m∠4= m∠5$.", "role": "user" }, { "content": "32", "role": "assistant" } ]
<image>Find the perimeter of the triangle. Round to the nearest tenth if necessary.
43.5
[ { "content": "<image>Find the perimeter of the triangle. Round to the nearest tenth if necessary.", "role": "user" }, { "content": "43.5", "role": "assistant" } ]
<image>If $\overline{QR} \| \overline{XY}, XQ=15, QZ=12$, and $YR=20$, what is the length of $\overline{RZ}$.
16
[ { "content": "<image>If $\\overline{QR} \\| \\overline{XY}, XQ=15, QZ=12$, and $YR=20$, what is the length of $\\overline{RZ}$.", "role": "user" }, { "content": "16", "role": "assistant" } ]
<image>Find $x$.
13.9
[ { "content": "<image>Find $x$.", "role": "user" }, { "content": "13.9", "role": "assistant" } ]
<image>In $\odot P$, $PS=4$, find the length of $\widehat {QR}$. Round to the nearest hundredth.
4.75
[ { "content": "<image>In $\\odot P$, $PS=4$, find the length of $\\widehat {QR}$. Round to the nearest hundredth.", "role": "user" }, { "content": "4.75", "role": "assistant" } ]
<image>Find $y$ if $\triangle JLM \sim \triangle QST$.
4
[ { "content": "<image>Find $y$ if $\\triangle JLM \\sim \\triangle QST$.", "role": "user" }, { "content": "4", "role": "assistant" } ]
<image>Find $MP$.
8
[ { "content": "<image>Find $MP$.", "role": "user" }, { "content": "8", "role": "assistant" } ]
<image>Find x.
24 \sqrt { 2 }
[ { "content": "<image>Find x.", "role": "user" }, { "content": "24 \\sqrt { 2 }", "role": "assistant" } ]
<image>For the pair of similar figures, use the given areas to find $x$.
10.4
[ { "content": "<image>For the pair of similar figures, use the given areas to find $x$.", "role": "user" }, { "content": "10.4", "role": "assistant" } ]
<image>Find the length of $\widehat {ZY}$. Round to the nearest hundredth.
5.24
[ { "content": "<image>Find the length of $\\widehat {ZY}$. Round to the nearest hundredth.", "role": "user" }, { "content": "5.24", "role": "assistant" } ]
<image>Find the value of x.
130
[ { "content": "<image>Find the value of x.", "role": "user" }, { "content": "130", "role": "assistant" } ]
<image>Find $m \angle A B C$ if $m \widehat{A B}=102$
129
[ { "content": "<image>Find $m \\angle A B C$ if $m \\widehat{A B}=102$", "role": "user" }, { "content": "129", "role": "assistant" } ]
<image>If $R T=15, Q P=21,$ and $P T=8,$ find $T S$
20
[ { "content": "<image>If $R T=15, Q P=21,$ and $P T=8,$ find $T S$", "role": "user" }, { "content": "20", "role": "assistant" } ]
<image>$\triangle K L N$ and $\triangle L M N$ are isosceles and $m \angle J K N=130$. Find the measure of $\angle LKN$.
81
[ { "content": "<image>$\\triangle K L N$ and $\\triangle L M N$ are isosceles and $m \\angle J K N=130$. Find the measure of $\\angle LKN$.", "role": "user" }, { "content": "81", "role": "assistant" } ]
<image>Find x. Round the side measure to the nearest tenth.
34.8
[ { "content": "<image>Find x. Round the side measure to the nearest tenth.", "role": "user" }, { "content": "34.8", "role": "assistant" } ]
<image>Find sinA
\sqrt { 26 } / 26
[ { "content": "<image>Find sinA", "role": "user" }, { "content": "\\sqrt { 26 } / 26", "role": "assistant" } ]
<image>If XM = 4, XN = 6, and NZ = 9, find XY.
10
[ { "content": "<image>If XM = 4, XN = 6, and NZ = 9, find XY.", "role": "user" }, { "content": "10", "role": "assistant" } ]
<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.
8
[ { "content": "<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "role": "user" }, { "content": "8", "role": "assistant" } ]
<image>Find $x$.
\frac { 26 } { 3 }
[ { "content": "<image>Find $x$.", "role": "user" }, { "content": "\\frac { 26 } { 3 }", "role": "assistant" } ]
<image>In the figure, $m∠1 = 50$ and $m∠3 = 60$. Find the measure of $\angle 2$.
110
[ { "content": "<image>In the figure, $m∠1 = 50$ and $m∠3 = 60$. Find the measure of $\\angle 2$.", "role": "user" }, { "content": "110", "role": "assistant" } ]
<image>Find the measure of $∠A$ to the nearest tenth.
16.7
[ { "content": "<image>Find the measure of $∠A$ to the nearest tenth.", "role": "user" }, { "content": "16.7", "role": "assistant" } ]
<image>Find x.
2 \sqrt { 13 }
[ { "content": "<image>Find x.", "role": "user" }, { "content": "2 \\sqrt { 13 }", "role": "assistant" } ]
<image>Find $ m ∠RSU $ so that $ m \parallel n $.
124
[ { "content": "<image>Find $ m ∠RSU $ so that $ m \\parallel n $.", "role": "user" }, { "content": "124", "role": "assistant" } ]
<image>Find tanB
5
[ { "content": "<image>Find tanB", "role": "user" }, { "content": "5", "role": "assistant" } ]
<image>$RP=3.5$ and $JP=9$. Find $PL$.
7
[ { "content": "<image>$RP=3.5$ and $JP=9$. Find $PL$.", "role": "user" }, { "content": "7", "role": "assistant" } ]
<image>If PR || WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find SY
4
[ { "content": "<image>If PR || WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find SY", "role": "user" }, { "content": "4", "role": "assistant" } ]
<image>Find x.
2 \sqrt { 5 }
[ { "content": "<image>Find x.", "role": "user" }, { "content": "2 \\sqrt { 5 }", "role": "assistant" } ]
<image>The sum of the circumference of circles $H,J,K$ is $56 \pi$ units. Find $KJ$.
24
[ { "content": "<image>The sum of the circumference of circles $H,J,K$ is $56 \\pi$ units. Find $KJ$.", "role": "user" }, { "content": "24", "role": "assistant" } ]
<image>Solve for x in the figure below.
7
[ { "content": "<image>Solve for x in the figure below.", "role": "user" }, { "content": "7", "role": "assistant" } ]
<image>Find the measure of $\angle 2$ if $m \angle D G F=53$ and $m \angle A G C=40$.
50
[ { "content": "<image>Find the measure of $\\angle 2$ if $m \\angle D G F=53$ and $m \\angle A G C=40$.", "role": "user" }, { "content": "50", "role": "assistant" } ]
<image>Find $x$.
4
[ { "content": "<image>Find $x$.", "role": "user" }, { "content": "4", "role": "assistant" } ]
<image>Find $m \angle D G E$
30
[ { "content": "<image>Find $m \\angle D G E$", "role": "user" }, { "content": "30", "role": "assistant" } ]
<image>Refer to the figure at the right. Find the value of $x$ if $ p \parallel q $.
45
[ { "content": "<image>Refer to the figure at the right. Find the value of $x$ if $ p \\parallel q $.", "role": "user" }, { "content": "45", "role": "assistant" } ]
<image>Find the length of $WY$
9
[ { "content": "<image>Find the length of $WY$", "role": "user" }, { "content": "9", "role": "assistant" } ]
<image>Find $m\angle U$
134
[ { "content": "<image>Find $m\\angle U$", "role": "user" }, { "content": "134", "role": "assistant" } ]
<image>$\Delta DFG$ and $\Delta F G H$ are isosceles, $m \angle FDH=28$ and$\overline{DG} \cong \overline{FG} \cong \overline{FH}$. Find the measure of $\angle GFH$.
68
[ { "content": "<image>$\\Delta DFG$ and $\\Delta F G H$ are isosceles, $m \\angle FDH=28$ and$\\overline{DG} \\cong \\overline{FG} \\cong \\overline{FH}$. Find the measure of $\\angle GFH$. ", "role": "user" }, { "content": "68", "role": "assistant" } ]
<image>Find y.
1.5
[ { "content": "<image>Find y.", "role": "user" }, { "content": "1.5", "role": "assistant" } ]
<image>If $\overline{PR} \| \overline{KL}, KN=9, LN=16,$ and $PM=2KP$, find $MN$.
12
[ { "content": "<image>If $\\overline{PR} \\| \\overline{KL}, KN=9, LN=16,$ and $PM=2KP$, find $MN$.", "role": "user" }, { "content": "12", "role": "assistant" } ]
<image>Find $NP$.
14
[ { "content": "<image>Find $NP$.", "role": "user" }, { "content": "14", "role": "assistant" } ]
<image>In the figure, $ \overline{JM} \cong \overline{PM}$ and $ \overline{ML} \cong \overline{PL}$. If $m \angle PLJ=34$, find $m \angle JPM$.
36.5
[ { "content": "<image>In the figure, $ \\overline{JM} \\cong \\overline{PM}$ and $ \\overline{ML} \\cong \\overline{PL}$. If $m \\angle PLJ=34$, find $m \\angle JPM$.", "role": "user" }, { "content": "36.5", "role": "assistant" } ]
<image>Find $x$.
12
[ { "content": "<image>Find $x$.", "role": "user" }, { "content": "12", "role": "assistant" } ]
<image>Find $x$.
135
[ { "content": "<image>Find $x$.", "role": "user" }, { "content": "135", "role": "assistant" } ]
<image>If $\overline{RQ} \cong \overline{RS}$ and $ m ∠RQS = 75 $, find $ m ∠R $.
30
[ { "content": "<image>If $\\overline{RQ} \\cong \\overline{RS}$ and $ m ∠RQS = 75 $, find $ m ∠R $.", "role": "user" }, { "content": "30", "role": "assistant" } ]
<image>Find $y$ in the figure.
40
[ { "content": "<image>Find $y$ in the figure.", "role": "user" }, { "content": "40", "role": "assistant" } ]
<image>Find x to the nearest tenth.
150
[ { "content": "<image>Find x to the nearest tenth.", "role": "user" }, { "content": "150", "role": "assistant" } ]
<image>Find $h$ in each triangle.
6 \sqrt 3
[ { "content": "<image>Find $h$ in each triangle.", "role": "user" }, { "content": "6 \\sqrt 3", "role": "assistant" } ]
<image>Find x.
10
[ { "content": "<image>Find x.", "role": "user" }, { "content": "10", "role": "assistant" } ]
<image>Find $x$.
18
[ { "content": "<image>Find $x$.", "role": "user" }, { "content": "18", "role": "assistant" } ]
<image>Find x.
\frac { 4 } { 9 } \sqrt { 3 }
[ { "content": "<image>Find x.", "role": "user" }, { "content": "\\frac { 4 } { 9 } \\sqrt { 3 }", "role": "assistant" } ]
<image>Trapezoid MNPQ has an area of 360 square feet. Find the length of $\overline{MN}$.
14
[ { "content": "<image>Trapezoid MNPQ has an area of 360 square feet. Find the length of $\\overline{MN}$.", "role": "user" }, { "content": "14", "role": "assistant" } ]
<image>Find x. Round side measures to the nearest tenth.
15.1
[ { "content": "<image>Find x. Round side measures to the nearest tenth.", "role": "user" }, { "content": "15.1", "role": "assistant" } ]
<image>Each pair of polygons is similar. Find CD
\frac { 10 } { 3 }
[ { "content": "<image>Each pair of polygons is similar. Find CD", "role": "user" }, { "content": "\\frac { 10 } { 3 }", "role": "assistant" } ]
<image>Find the area of the shaded sector. Round to the nearest tenth.
7.4
[ { "content": "<image>Find the area of the shaded sector. Round to the nearest tenth.", "role": "user" }, { "content": "7.4", "role": "assistant" } ]
<image>If $\frac{I J}{X J}=\frac{HJ}{YJ}, m \angle W X J=130$, and $m \angle WZG=20,$ find $m \angle JIH$
50
[ { "content": "<image>If $\\frac{I J}{X J}=\\frac{HJ}{YJ}, m \\angle W X J=130$, and $m \\angle WZG=20,$ find $m \\angle JIH$", "role": "user" }, { "content": "50", "role": "assistant" } ]
<image>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 $q$.
7
[ { "content": "<image>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 $q$.", "role": "user" }, { "content": "7", "role": "assistant" } ]
<image>Find x
5 \sqrt { 3 }
[ { "content": "<image>Find x", "role": "user" }, { "content": "5 \\sqrt { 3 }", "role": "assistant" } ]
<image>$a=14, b=48,$ and $c=50$ find $cosB$
0.28
[ { "content": "<image>$a=14, b=48,$ and $c=50$ find $cosB$", "role": "user" }, { "content": "0.28", "role": "assistant" } ]
<image>Find $x$.
9
[ { "content": "<image>Find $x$.", "role": "user" }, { "content": "9", "role": "assistant" } ]
<image>$\triangle ABC$ is an isosceles triangle with base $BC$. What is the perimeter of the triangle?
40
[ { "content": "<image>$\\triangle ABC$ is an isosceles triangle with base $BC$. What is the perimeter of the triangle?", "role": "user" }, { "content": "40", "role": "assistant" } ]
<image>$\overline{XY}$ and $\overline{XZ}$ are midsegments of $\triangle RST$. Find $m \angle RYX$.
124
[ { "content": "<image>$\\overline{XY}$ and $\\overline{XZ}$ are midsegments of $\\triangle RST$. Find $m \\angle RYX$.", "role": "user" }, { "content": "124", "role": "assistant" } ]
<image>Find x. Assume that segments that appear to be tangent are tangent.
4
[ { "content": "<image>Find x. Assume that segments that appear to be tangent are tangent.", "role": "user" }, { "content": "4", "role": "assistant" } ]
<image>Find the perimeter of trapezoid PQRS..
38 + 6 \sqrt { 2 } + 6 \sqrt { 3 }
[ { "content": "<image>Find the perimeter of trapezoid PQRS..", "role": "user" }, { "content": "38 + 6 \\sqrt { 2 } + 6 \\sqrt { 3 }", "role": "assistant" } ]
<image>Find $m\angle 3$.
99
[ { "content": "<image>Find $m\\angle 3$.", "role": "user" }, { "content": "99", "role": "assistant" } ]
<image>Find $m\angle S$
123
[ { "content": "<image>Find $m\\angle S$", "role": "user" }, { "content": "123", "role": "assistant" } ]
<image>Find x.
4 \sqrt { 3 }
[ { "content": "<image>Find x.", "role": "user" }, { "content": "4 \\sqrt { 3 }", "role": "assistant" } ]
<image>Find $y$ so that the quadrilateral is a parallelogram.
9
[ { "content": "<image>Find $y$ so that the quadrilateral is a parallelogram.", "role": "user" }, { "content": "9", "role": "assistant" } ]
<image>Find $x$.
107
[ { "content": "<image>Find $x$.", "role": "user" }, { "content": "107", "role": "assistant" } ]
<image>$m∠11 = 4x$, $m∠12 = 2x -6 $. Find the measure of $\angle 12$.
56
[ { "content": "<image>$m∠11 = 4x$, $m∠12 = 2x -6 $. Find the measure of $\\angle 12$.", "role": "user" }, { "content": "56", "role": "assistant" } ]
<image>Find $m \angle TUV$
53
[ { "content": "<image>Find $m \\angle TUV$", "role": "user" }, { "content": "53", "role": "assistant" } ]
<image>Find x
6
[ { "content": "<image>Find x", "role": "user" }, { "content": "6", "role": "assistant" } ]
<image>Find x
4 \sqrt { 6 }
[ { "content": "<image>Find x", "role": "user" }, { "content": "4 \\sqrt { 6 }", "role": "assistant" } ]
<image>If $m\angle BAD = 38$ and $m\angle BCD = 50$, find $m\angle ADC$.
146
[ { "content": "<image>If $m\\angle BAD = 38$ and $m\\angle BCD = 50$, find $m\\angle ADC$.", "role": "user" }, { "content": "146", "role": "assistant" } ]
<image>Find $m \angle 5$.
110
[ { "content": "<image>Find $m \\angle 5$.", "role": "user" }, { "content": "110", "role": "assistant" } ]
<image>Find the perimeter or circumference of the figure. Round to the nearest tenth.
25.1
[ { "content": "<image>Find the perimeter or circumference of the figure. Round to the nearest tenth.", "role": "user" }, { "content": "25.1", "role": "assistant" } ]
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