Datasets:
xyliu6
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geometry3k

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1
images
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1
1
problem
stringlengths
13
234
answer
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34
id
int64
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2.1k
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ground_truth
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4 values
<image>Find x
18
854
[ "16", "18", "24", "27" ]
B
<image>Find $x$ so that $ m \parallel n $.
15
28
[ "7", "9", "11", "15" ]
D
<image>Find the area of the figure. Round to the nearest tenth if necessary.
500
847
[ "92.5", "250", "500", "1000" ]
C
<image>Find $m\angle C$
127
2,020
[ "112", "116", "117", "127" ]
D
<image>Use parallelogram ABCD to find CD
6
890
[ "6", "9", "12", "18" ]
A
<image>Find $y$.
73.5
1,524
[ "56", "65", "73.5", "115" ]
C
<image>Find the area of the figure. Round to the nearest hundredth, if necessary.
68.6
1,734
[ "33.6", "48", "58.6", "68.6" ]
D
<image>Find $RT$.
10
285
[ "6", "8", "10", "12" ]
C
<image>Find the area of the shaded region. Round to the nearest tenth.
471.2
480
[ "392.7", "471.2", "589.0", "785.4" ]
B
<image>Find the measure of $\angle 2$.
53
731
[ "53", "63", "73", "83" ]
A
<image>Find x.
5
916
[ "\\frac { 5 } { 2 } \\sqrt { 2 }", "5", "\\frac { 5 } { 2 } \\sqrt { 6 }", "10" ]
B
<image>Find $x$ so that each quadrilateral is a parallelogram.
8
964
[ "8", "22", "24", "40" ]
A
<image>Each pair of polygons is similar. Find x
30
315
[ "30", "70", "80", "150" ]
A
<image>Find the value of the variable $x$ in the figure.
63
1,653
[ "27", "54", "63", "126" ]
C
<image>In the figure, $m ∠9 = 75$. Find the measure of $\angle 3$.
75
1,419
[ "75", "85", "95", "105" ]
A
<image>Find $x$.
75
1,478
[ "60", "65", "70", "75" ]
D
<image>Find x. Round to the nearest tenth.
57.2
1,666
[ "11.8", "29.2", "51.0", "57.2" ]
D
<image>Find $m\angle L$
52
589
[ "52", "62", "96", "150" ]
A
<image>In the figure, $m∠3 = 43$. Find the measure of $\angle 2$.
137
420
[ "43", "127", "137", "147" ]
C
<image>Find $x$ so that $ m \parallel n $.
15
1,334
[ "7", "11", "15", "19" ]
C
<image>The pair of polygons is similar. Find AB
4
1,103
[ "3", "4", "5", "6" ]
B
<image>Use parallelogram $ABCD$ to find the measure of $m\angle ADC$
65
180
[ "21", "65", "105", "115" ]
B
<image>$a=14, b=48,$ and $c=50$, find $sinB$
0.96
1,511
[ "0.04", "0.48", "0.50", "0.96" ]
D
<image>Find $m \angle 3$.
68
1,759
[ "56", "56", "68", "78" ]
C
<image>Find x. Round to the nearest tenth.
10.8
309
[ "3.4", "4.3", "10.8", "13.7" ]
C
<image>$ \triangle RST$ is a right triangle. Find $m∠R$.
60
1,182
[ "30", "40", "50", "60" ]
D
<image>Use parallelogram ABCD to find AF
6.86
1,693
[ "6", "6.86", "9", "13.62" ]
B
<image>Find $m \angle C$.
47
1,850
[ "17", "20", "33", "47" ]
D
<image>$\triangle MHJ \cong \triangle PQJ$. Find $y$.
5
862
[ "3", "4", "5", "6" ]
C
<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.
50
1,558
[ "25", "30", "40", "50" ]
D
<image>If $\overline{PR} \| \overline{KL}, KN=9, LN=16,$ and $PM=2KP$, find $ML$.
20
244
[ "15", "16", "20", "24" ]
C
<image>Find x
4
1,670
[ "3", "4", "6", "7" ]
B
<image>In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\angle 4$.
62
1,618
[ "38", "62", "118", "142" ]
B
<image>If $LK=4,MP=3,PQ=6,KJ=2,RS=6$, and $LP=2$, find $QK$.
6
721
[ "2", "3", "4", "6" ]
D
<image>Find $x$.
13
925
[ "9", "13", "16", "22" ]
B
<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
211
[ "25", "30", "40", "50" ]
D
<image>Find the perimeter of $▱ TRVW$.
60
541
[ "30", "48", "60", "72" ]
C
<image>Find $x$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.
5.6
1,803
[ "4", "5.6", "6", "8" ]
B
<image>In the figure, $QR \| TS$, $QT \| RS$, and $m \angle 1=131$. Find the measure of $\angle 7$.
49
714
[ "39", "49", "59", "131" ]
B
<image>Find $m \angle 2$.
52
1,388
[ "29", "52", "57", "123" ]
B
<image>Find $m\angle J$
112
617
[ "102", "107", "112", "117" ]
C
<image>Find the length of $\widehat {AB}$. Round to the nearest hundredth.
2.36
34
[ "1.18", "2.36", "3.36", "4.72" ]
B
<image>If $LK=4,MP=3,PQ=6,KJ=2,RS=6$, and $LP=2$, find $QR$.
3
1,062
[ "2", "3", "4", "6" ]
B
<image>Find $m \angle 4$.
40
1,833
[ "20", "30", "40", "65" ]
C
<image>Find $m\angle 3$.
12
438
[ "12", "17", "61", "151" ]
A
<image>Find $m \widehat {WX}$.
66
1,003
[ "57", "63", "66", "68" ]
C
<image>Find $m \angle 2$.
24
1,736
[ "12", "24", "38", "66" ]
B
<image>Quadrilateral $A B C D$ is inscribed in $\odot Z$ such that $m \angle B Z A=104, m \widehat{C B}=94,$ and $\overline{A B} \| \overline{D C} .$ Find $m \widehat{A D C}$
162
1,128
[ "36", "90", "120", "162" ]
D
<image>In $\odot O, \overline{E C}$ and $\overline{A B}$ are diameters, and $\angle B O D \cong \angle D O E \cong \angle E O F \cong \angle F O A$ Find $m\widehat{E B}$
90
1,554
[ "45", "90", "180", "360" ]
B
<image>Use parallelogram MNPR to find $w$
3.5
1,631
[ "3.5", "11", "11.1", "14" ]
A
<image>Find the area of the triangle. Round to the nearest hundredth.
6.79
1,332
[ "3.88", "6.79", "13.58", "14" ]
B
<image>The two polygons are similar. Then find y.
20.5
1,955
[ "18", "20.5", "38", "199" ]
B
<image>Find the measure of the altitude drawn to the hypotenuse.
5
1,950
[ "\\sqrt { 2.5 }", "2", "\\sqrt { 10 }", "5" ]
D
<image>For isosceles trapezoid $A B C D$, $X$ and $Y$ are midpoints of the legs. Find $m \angle X B C$ if $m \angle A D Y=78$
102
1,999
[ "39", "51", "78", "102" ]
D
<image>Find the exact value of $DE,$ given $AD=12$ and $BD=4$
2 \sqrt { 3 }
234
[ "2 \\sqrt { 3 }", "2 \\sqrt { 6 }", "4 \\sqrt { 3 }", "4 \\sqrt { 6 }" ]
A
<image>If $\overline{TU} \perp \overline{UV}$ and $\overline{UV} \perp \overline{VW}$, find $m \angle 1$.
45
869
[ "45", "47", "52", "55" ]
A
<image>Circles $G, J,$ and $K$ all intersect at $L$ If $G H=10,$ find GL.
10
644
[ "10", "20", "25", "35" ]
A
<image>Find $m\angle V$
193
1,423
[ "34", "68", "193", "213" ]
C
<image>Find the measure of $\angle 4$ in the figure.
60
1,084
[ "52", "56", "58", "60" ]
D
<image>What is the length of $\overline{EF}$?
26
1,537
[ "13", "14.5", "26", "29" ]
C
<image>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 $y$.
4
393
[ "3", "4", "5", "6" ]
B
<image>Find the area of the figure. Round to the nearest tenth.
87.5
1,647
[ "49", "68.2", "87.5", "126.0" ]
C
<image>Find $m \angle A G E$
120
1,596
[ "60", "120", "210", "330" ]
B
<image>Polygon ABCD ~ polygon AEFG, $m\angle AGF = 108$, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find the perimeter of trapezoid AEFG
45.75
379
[ "4.575", "12", "26", "45.75" ]
D
<image>What is the value of x in the figure below?
7
856
[ "5", "7", "8", "10" ]
B
<image>Find the area of a regular hexagon with a perimeter of 72 feet.
374.1
1,096
[ "187.1", "305.5", "374.1", "532" ]
C
<image>Find the length of $CB$ in the isosceles triangle ABC.
7
637
[ "1.5", "7", "11", "12.5" ]
B
<image>Find the measure of $\angle R$
122
172
[ "5", "40", "78", "122" ]
D
<image>Find the perimeter of the triangle.
100.4
759
[ "87", "90", "95", "100.4" ]
D
<image>$ABCD$ is a rhombus. If $PB = 12$, $AB = 15$, and $m\angle ABD = 24$, Find $CP$
9
492
[ "3", "6", "9", "15" ]
C
<image>$\overline{XY}$ and $\overline{XZ}$ are midsegments of $\triangle RST$. Find $m \angle RYX$.
124
1,357
[ "110", "124", "126", "134" ]
B
<image>Find x. Assume that segments that appear to be tangent are tangent.
30
177
[ "15", "20", "15 \\sqrt { 3 }", "30" ]
D
<image>Find $E D$ if $A B=6, B C=4,$ and $A E=9$
6
618
[ "3", "6", "9", "13.5" ]
B
<image>Find $XA$.
4
943
[ "2", "4", "8", "16" ]
B
<image>Find the area of a regular pentagon with a perimeter of 40 centimeters.
110
1,437
[ "88", "110", "132", "160" ]
B
<image>Find $RS$.
25
560
[ "5", "15", "20", "25" ]
D
<image>Find DE
6
316
[ "6", "8", "9", "11" ]
A
<image>Find x
39.8
2,058
[ "39.8", "42.5", "67.8", "68.9" ]
A
<image>Find $KL$.
6
1,032
[ "3", "6", "12", "18" ]
B
<image>Find the measure of $\angle T$.
77
214
[ "60", "77", "103", "154" ]
B
<image>Find y.
4 \sqrt { 6 }
598
[ "4 \\sqrt { 2 }", "4 \\sqrt { 3 }", "4 \\sqrt { 6 }", "8 \\sqrt { 6 }" ]
C
<image>Quadrilateral $ABCD$ is a rhombus. If $m\angle DPC = 3x – 15$, find $x$.
35
267
[ "14", "35", "56", "90" ]
B
<image>In $\triangle RST$, $Z$ is the centroid and $RZ=18$. Find $SR$.
28
1,013
[ "10", "14", "18", "28" ]
D
<image>Find x
37
448
[ "26", "37", "80", "89" ]
B
<image>Find the perimeter of $▱ JKLM$.
22.4
39
[ "11.2", "22.4", "24", "44.8" ]
B
<image>find $cosR$
0.6
258
[ "0.2", "0.4", "0.6", "0.8" ]
C
<image>In the figure, $m∠8 = 96$ and $m∠12 = 42$. Find the measure of $\angle 6$.
42
129
[ "42", "48", "84", "96" ]
A
<image>Find $JL$.
12
933
[ "3", "6", "12", "24" ]
C
<image>Find $h$ in each triangle.
\frac { 15 \sqrt 2 } { 2 }
169
[ "\\frac { 15 \\sqrt 2 } { 3 }", "\\frac { 15 } { 2 }", "\\frac { 15 \\sqrt 2 } { 2 }", "15" ]
C
<image>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?
0.44
1,732
[ "0.08", "0.22", "0.44", "0.77" ]
C
<image>Find the area of the figure. Round to the nearest tenth if necessary.
63.2
607
[ "5.9", "57.3", "63.2", "69.1" ]
C
<image>In $\odot R, S U=20, Y W=20,$ and $m \widehat{Y X}=45$. Find $m\widehat{S U}$
90
2,079
[ "20", "30", "45", "90" ]
D
<image>Find $DB$.
5
1,010
[ "3", "5", "12", "15" ]
B
<image>Circle $O$ has a radius of $10, A B=10$ and $m \overrightarrow{A B}=60 .$ Find $m\widehat{O X}$
5 \sqrt { 3 }
786
[ "5", "5 \\sqrt { 3 }", "10", "15" ]
B
<image>Find the value of the variable $x$ in the figure.
70
1,238
[ "46.7", "60", "70", "80" ]
C
<image>Quadrilateral DEFG is a rectangle. If $FD = 3x - 7$ and $EG = x + 5$, find $EG$.
6
906
[ "6", "12", "34", "56" ]
A
<image>$\triangle ABC \cong \triangle FGH$. Find $x$.
3
653
[ "2", "3", "7", "13" ]
B
<image>$\triangle RST \cong \triangle VUT$. Find $x$.
2
122
[ "1", "2", "3", "4" ]
B
<image>Find $x$.
6
80
[ "5", "6", "10", "12" ]
B
<image>Find the value of x.
8
1,658
[ "6", "7", "8", "9" ]
C