Datasets:
mm-eval
/
Geometry3K

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1
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2 values
tra_00800
[{"role": "user", "question": "<image>Find y", "hint": "", "options": {}, "choices": []}]
4 \sqrt { 3 }
open
tra_00801
[{"role": "user", "question": "<image>Find $x$.", "hint": "", "options": {}, "choices": []}]
66
numeric
tra_00802
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
17
numeric
tra_00803
[{"role": "user", "question": "<image>Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
30.4
numeric
tra_00804
[{"role": "user", "question": "<image>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 $C$.", "hint": "", "options": {}, "choices": []}]
17
numeric
tra_00805
[{"role": "user", "question": "<image>Find y. Round to the nearest tenth, if necessary.", "hint": "", "options": {}, "choices": []}]
22.5
numeric
tra_00806
[{"role": "user", "question": "<image>Find y", "hint": "", "options": {}, "choices": []}]
4 \sqrt { 3 }
open
tra_00807
[{"role": "user", "question": "<image>Find $XZ$ of isosceles $\\triangle XYZ$", "hint": "", "options": {}, "choices": []}]
12
numeric
tra_00808
[{"role": "user", "question": "<image>Find $m \\angle 2$.", "hint": "", "options": {}, "choices": []}]
24
numeric
tra_00809
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
0.5
numeric
tra_00810
[{"role": "user", "question": "<image>If $J,P,$ and $L$ are the midpoints of $\\overline{KH}, \\overline{HM}$ and $\\overline{MK}$, respectively. Find $x$.", "hint": "", "options": {}, "choices": []}]
4.75
numeric
tra_00811
[{"role": "user", "question": "<image>If $ABCDE \\sim PQRST,$ find the scale factor of $ABCDE$ to $PQRST$.", "hint": "", "options": {}, "choices": []}]
\frac { 4 } { 3 }
open
tra_00812
[{"role": "user", "question": "<image>Quadrilateral DEFG is a rectangle. If $FD = 3x - 7$ and $EG = x + 5$, find $EG$.", "hint": "", "options": {}, "choices": []}]
6
numeric
tra_00813
[{"role": "user", "question": "<image>Find the value of $x$ in the figure below.", "hint": "", "options": {}, "choices": []}]
128
numeric
tra_00814
[{"role": "user", "question": "<image>If KLMN is a parallelogram, find the value of the\r\nindicated variable. Find y", "hint": "", "options": {}, "choices": []}]
11
numeric
tra_00815
[{"role": "user", "question": "<image>What is the length of $R T ?$", "hint": "", "options": {}, "choices": []}]
5 \sqrt { 2 }
open
tra_00816
[{"role": "user", "question": "<image>Find $\\angle 8$", "hint": "", "options": {}, "choices": []}]
90
numeric
tra_00817
[{"role": "user", "question": "<image>What is the perimeter of the figure?", "hint": "", "options": {}, "choices": []}]
20
numeric
tra_00818
[{"role": "user", "question": "<image>Find $x$.", "hint": "", "options": {}, "choices": []}]
70
numeric
tra_00819
[{"role": "user", "question": "<image>Find the measure of $\\angle A$. Round to the nearest degree.", "hint": "", "options": {}, "choices": []}]
74
numeric
tra_00820
[{"role": "user", "question": "<image>Find $m\\angle B$", "hint": "", "options": {}, "choices": []}]
112
numeric
tra_00821
[{"role": "user", "question": "<image>Find y. Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
11.7
numeric
tra_00822
[{"role": "user", "question": "<image>Use a calculator to find the measure of $∠J$ to the nearest degree.", "hint": "", "options": {}, "choices": []}]
45
numeric
tra_00823
[{"role": "user", "question": "<image>Express the ratio of $\\sin A$ as a decimal to the nearest hundredth.", "hint": "", "options": {}, "choices": []}]
0.80
numeric
tra_00824
[{"role": "user", "question": "<image>WXYZ is a square. If $WT = 3$, find $m \\angle WTZ$", "hint": "", "options": {}, "choices": []}]
90
numeric
tra_00825
[{"role": "user", "question": "<image>Find x", "hint": "", "options": {}, "choices": []}]
18
numeric
tra_00826
[{"role": "user", "question": "<image>In the figure, $m ∠9 = 75$. Find the measure of $\\angle 12$.", "hint": "", "options": {}, "choices": []}]
105
numeric
tra_00827
[{"role": "user", "question": "<image>Find $m \\widehat{Y C}$.", "hint": "", "options": {}, "choices": []}]
60
numeric
tra_00828
[{"role": "user", "question": "<image>Find the perimeter of the figure. Round to the nearest hundredth, if necessary.", "hint": "", "options": {}, "choices": []}]
9.2
numeric
tra_00829
[{"role": "user", "question": "<image>In $\\odot R, S U=20, Y W=20,$ and $m \\widehat{Y X}=45$.\r\nFind WZ", "hint": "", "options": {}, "choices": []}]
10
numeric
tra_00830
[{"role": "user", "question": "<image>$a=14, b=48,$ and $c=50$ find $tanA$", "hint": "", "options": {}, "choices": []}]
0.29
numeric
tra_00831
[{"role": "user", "question": "<image>Find $R S$ if $P Q=12, Q R=2,$ and $T S=3$", "hint": "", "options": {}, "choices": []}]
4
numeric
tra_00832
[{"role": "user", "question": "<image>Use parallelogram JKLM to find m \\angle JKL if $J K=2 b+3$ and $J M=3 a$.", "hint": "", "options": {}, "choices": []}]
80
numeric
tra_00833
[{"role": "user", "question": "<image>Find $m \\angle 7$.", "hint": "", "options": {}, "choices": []}]
70
numeric
tra_00834
[{"role": "user", "question": "<image>Find $RS$.", "hint": "", "options": {}, "choices": []}]
8
numeric
tra_00835
[{"role": "user", "question": "<image>Find the area of the figure to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
87.5
numeric
tra_00836
[{"role": "user", "question": "<image>Find x. Round side measures to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
7.7
numeric
tra_00837
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
85
numeric
tra_00838
[{"role": "user", "question": "<image>Find the area of the figure. Round to the nearest tenth if necessary.", "hint": "", "options": {}, "choices": []}]
63.2
numeric
tra_00839
[{"role": "user", "question": "<image>Find x", "hint": "", "options": {}, "choices": []}]
60
numeric
tra_00840
[{"role": "user", "question": "<image>Which of the following statements about the figure is true?", "hint": "", "options": {}, "choices": []}]
a + b = 90
open
tra_00841
[{"role": "user", "question": "<image>$\\overline{JH}, \\overline{JP},$ and $\\overline{PH}$ are midsegments of $\\triangle KLM$. Find $x$.", "hint": "", "options": {}, "choices": []}]
57
numeric
tra_00842
[{"role": "user", "question": "<image>$Q$ is the incenter of $\\triangle JKL$. Find $m \\angle QJK$.", "hint": "", "options": {}, "choices": []}]
35
numeric
tra_00843
[{"role": "user", "question": "<image>In $\\odot S, m \\angle T S R=42$\r\nFind $m\\widehat{KT}$", "hint": "", "options": {}, "choices": []}]
138
numeric
tra_00844
[{"role": "user", "question": "<image>Find the measure of $\\angle 2$.", "hint": "", "options": {}, "choices": []}]
25
numeric
tra_00845
[{"role": "user", "question": "<image>Find $y$ in the figure.", "hint": "", "options": {}, "choices": []}]
15
numeric
tra_00846
[{"role": "user", "question": "<image>Quadrilateral ABCD is a rhombus. If $m\\angle BCD$ = 64, find $m\\angle BAC$.", "hint": "", "options": {}, "choices": []}]
32
numeric
tra_00847
[{"role": "user", "question": "<image>Find the area of the shaded sector. Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
1.5
numeric
tra_00848
[{"role": "user", "question": "<image>Find $GH$", "hint": "", "options": {}, "choices": []}]
39
numeric
tra_00849
[{"role": "user", "question": "<image>Find $x$.", "hint": "", "options": {}, "choices": []}]
3
numeric
tra_00850
[{"role": "user", "question": "<image>In the figure, $ \\overline{JM} \\cong \\overline{PM}$ and $ \\overline{ML} \\cong \\overline{PL}$. If $m \\angle PLJ=58$, find $m \\angle PJL$.", "hint": "", "options": {}, "choices": []}]
30.5
numeric
tra_00851
[{"role": "user", "question": "<image>Find $m\\angle 3$", "hint": "", "options": {}, "choices": []}]
32
numeric
tra_00852
[{"role": "user", "question": "<image>What is the value of $x$ if $m \\widehat{NR}=62$ and $m \\widehat {NP}=108$?", "hint": "", "options": {}, "choices": []}]
64
numeric
tra_00853
[{"role": "user", "question": "<image>Find y.", "hint": "", "options": {}, "choices": []}]
4 \sqrt { 6 }
open
tra_00854
[{"role": "user", "question": "<image>Find $m\\angle E$", "hint": "", "options": {}, "choices": []}]
158
numeric
tra_00855
[{"role": "user", "question": "<image>For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.", "hint": "", "options": {}, "choices": []}]
\frac { 1 } { \sqrt { 3 } }
open
tra_00856
[{"role": "user", "question": "<image>Find x. Round the side measure to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
22.8
numeric
tra_00857
[{"role": "user", "question": "<image>Find x", "hint": "", "options": {}, "choices": []}]
29.1
numeric
tra_00858
[{"role": "user", "question": "<image>Find $x$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "hint": "", "options": {}, "choices": []}]
6
numeric
tra_00859
[{"role": "user", "question": "<image>Find $m \\angle 2$.", "hint": "", "options": {}, "choices": []}]
52
numeric
tra_00860
[{"role": "user", "question": "<image>Quadrilateral WXYZ is a rectangle. If $XZ = 2c$ and $ZY = 6$, and $XY = 8$, find $WY$.", "hint": "", "options": {}, "choices": []}]
10
numeric
tra_00861
[{"role": "user", "question": "<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "hint": "", "options": {}, "choices": []}]
50
numeric
tra_00862
[{"role": "user", "question": "<image>Find $y$ so that the quadrilateral is a parallelogram.", "hint": "", "options": {}, "choices": []}]
20
numeric
tra_00863
[{"role": "user", "question": "<image>Find x", "hint": "", "options": {}, "choices": []}]
45
numeric
tra_00864
[{"role": "user", "question": "<image>Find $h$ in the triangle.", "hint": "", "options": {}, "choices": []}]
3 \sqrt 2
open
tra_00865
[{"role": "user", "question": "<image>Find $x$. Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
4.8
numeric
tra_00866
[{"role": "user", "question": "<image>Find $DB$.", "hint": "", "options": {}, "choices": []}]
9.2
numeric
tra_00867
[{"role": "user", "question": "<image>Use parallelogram ABCD to find $m\\angle DAC$", "hint": "", "options": {}, "choices": []}]
72
numeric
tra_00868
[{"role": "user", "question": "<image>Quadrilateral ABCD is a rectangle. Find x", "hint": "", "options": {}, "choices": []}]
5
numeric
tra_00869
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
48
numeric
tra_00870
[{"role": "user", "question": "<image>Find y.", "hint": "", "options": {}, "choices": []}]
1
numeric
tra_00871
[{"role": "user", "question": "<image>In $\\odot X, A B=30, C D=30,$ and $m \\widehat{C Z}=40$\r\nFind $m\\widehat{D Z}$", "hint": "", "options": {}, "choices": []}]
40
numeric
tra_00872
[{"role": "user", "question": "<image>Find $m \\angle 1$.", "hint": "", "options": {}, "choices": []}]
65
numeric
tra_00873
[{"role": "user", "question": "<image>Refer to the figure at the right. Find z.", "hint": "", "options": {}, "choices": []}]
11.09
numeric
tra_00874
[{"role": "user", "question": "<image>$A E$ is a tangent. If $A D=12$ and $F E=18$, how long is $A E$ to the nearest tenth unit?", "hint": "", "options": {}, "choices": []}]
27.5
numeric
tra_00875
[{"role": "user", "question": "<image>Find $\\angle V$", "hint": "", "options": {}, "choices": []}]
46
numeric
tra_00876
[{"role": "user", "question": "<image>Find $m\\angle J$", "hint": "", "options": {}, "choices": []}]
112
numeric
tra_00877
[{"role": "user", "question": "<image>Find $y$ so that the quadrilateral is a parallelogram", "hint": "", "options": {}, "choices": []}]
5
numeric
tra_00878
[{"role": "user", "question": "<image>Find the measure of $\\angle 3$ if $m∠DGF = 53$ and $m∠AGC = 40$.", "hint": "", "options": {}, "choices": []}]
50
numeric
tra_00879
[{"role": "user", "question": "<image>Find $y$.", "hint": "", "options": {}, "choices": []}]
13
numeric
tra_00880
[{"role": "user", "question": "<image>WXYZ is a square. If $WT = 3$, find $ZX$", "hint": "", "options": {}, "choices": []}]
6
numeric
tra_00881
[{"role": "user", "question": "<image>For trapezoid QRST, M and P are midpoints of the legs. If PM = 2x, QR = 3x, and TS = 10, find PM.", "hint": "", "options": {}, "choices": []}]
20
numeric
tra_00882
[{"role": "user", "question": "<image>Find $y$ so that the quadrilateral is a parallelogram.", "hint": "", "options": {}, "choices": []}]
8
numeric
tra_00883
[{"role": "user", "question": "<image>$\\overline{E D}$ is tangent to $\\odot F$ at point $E .$ Find $x$", "hint": "", "options": {}, "choices": []}]
5
numeric
tra_00884
[{"role": "user", "question": "<image>Use parallelogram NQRM to find NQ", "hint": "", "options": {}, "choices": []}]
14
numeric
tra_00885
[{"role": "user", "question": "<image>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 $m\\widehat{W V}$", "hint": "", "options": {}, "choices": []}]
76
numeric
tra_00886
[{"role": "user", "question": "<image>Find the area of the figure. Round to the nearest tenth if necessary.", "hint": "", "options": {}, "choices": []}]
374.5
numeric
tra_00887
[{"role": "user", "question": "<image>Find the measure of $\\angle 2$ in the figure.", "hint": "", "options": {}, "choices": []}]
52
numeric
tra_00888
[{"role": "user", "question": "<image>Quadrilateral $ABDC$ is a rectangle. Find $m \\angle 5 if $ m\\angle 1 = 38$. $", "hint": "", "options": {}, "choices": []}]
104
numeric
tra_00889
[{"role": "user", "question": "<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "hint": "", "options": {}, "choices": []}]
170
numeric
tra_00890
[{"role": "user", "question": "<image>Find $m\\angle V$", "hint": "", "options": {}, "choices": []}]
193
numeric
tra_00891
[{"role": "user", "question": "<image>In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\\angle 8$.", "hint": "", "options": {}, "choices": []}]
62
numeric
tra_00892
[{"role": "user", "question": "<image>Find $ST$.", "hint": "", "options": {}, "choices": []}]
5
numeric
tra_00893
[{"role": "user", "question": "<image>Find the perimeter of $\\triangle D E F$ if $\\triangle D E F \\sim \\triangle G F H$.", "hint": "", "options": {}, "choices": []}]
12.75
numeric
tra_00894
[{"role": "user", "question": "<image>Find ST", "hint": "", "options": {}, "choices": []}]
\frac { 50 } { 3 }
open
tra_00895
[{"role": "user", "question": "<image>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 $XV$.", "hint": "", "options": {}, "choices": []}]
4
numeric
tra_00896
[{"role": "user", "question": "<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 $\\overline{A B} \\| \\overline{D C} .$\r\nFind $m \\widehat{A D C}$", "hint": "", "options": {}, "choices": []}]
162
numeric
tra_00897
[{"role": "user", "question": "<image>If $m \\angle 1=3 x+40$, $m \\angle 2=2(y-10)$, and $m \\angle 3=2 x+70$, find $y$.", "hint": "", "options": {}, "choices": []}]
75
numeric
tra_00898
[{"role": "user", "question": "<image>Find $m \\angle 5$.", "hint": "", "options": {}, "choices": []}]
55
numeric
tra_00899
[{"role": "user", "question": "<image>Find $y$.", "hint": "", "options": {}, "choices": []}]
10
numeric