Datasets:
mm-eval
/
Geometry3K

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2 values
tra_02000
[{"role": "user", "question": "<image>Find x. Round to the nearest degree.", "hint": "", "options": {}, "choices": []}]
63
numeric
tra_02001
[{"role": "user", "question": "<image>Find $m \\angle F$.", "hint": "", "options": {}, "choices": []}]
30
numeric
tra_02002
[{"role": "user", "question": "<image>In $\\triangle ABC, \\overline{BD}$ is a median. If $AD=3x+5$ and $CD=5x-1,$ find $AC$.", "hint": "", "options": {}, "choices": []}]
28
numeric
tra_02003
[{"role": "user", "question": "<image>WXYZ is a parallelogram. Find $m \\angle X W Z$ ", "hint": "", "options": {}, "choices": []}]
65
numeric
tra_02004
[{"role": "user", "question": "<image>In $\\odot R, S U=20, Y W=20,$ and $m \\widehat{Y X}=45$.\r\nFind $m\\widehat{S U}$", "hint": "", "options": {}, "choices": []}]
90
numeric
tra_02005
[{"role": "user", "question": "<image>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", "hint": "", "options": {}, "choices": []}]
108
numeric
tra_02006
[{"role": "user", "question": "<image>Find $y$ in the figure.", "hint": "", "options": {}, "choices": []}]
28
numeric
tra_02007
[{"role": "user", "question": "<image>Find $y$.", "hint": "", "options": {}, "choices": []}]
1
numeric
tra_02008
[{"role": "user", "question": "<image>Refer to trapezoid $CDFG$ with median $\\overline{HE}$. Let $\\overline{WX}$ be the median of $CDEH$. Find $WX$.", "hint": "", "options": {}, "choices": []}]
42
numeric
tra_02009
[{"role": "user", "question": "<image>Find the measure of the altitude drawn to the hypotenuse", "hint": "", "options": {}, "choices": []}]
12
numeric
tra_02010
[{"role": "user", "question": "<image>Find x", "hint": "", "options": {}, "choices": []}]
17.1
numeric
tra_02011
[{"role": "user", "question": "<image>Find $\\angle B$ of quadrilateral ABCD", "hint": "", "options": {}, "choices": []}]
90
numeric
tra_02012
[{"role": "user", "question": "<image>Each pair of polygons is similar. Find y", "hint": "", "options": {}, "choices": []}]
7
numeric
tra_02013
[{"role": "user", "question": "<image>Find x. Assume that any segment that appears to be tangent is tangent.", "hint": "", "options": {}, "choices": []}]
210
numeric
tra_02014
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
\frac { 3 } { 2 } \sqrt { 3 }
open
tra_02015
[{"role": "user", "question": "<image>$a=8, b=15,$ and $c=17$, find $sinA$", "hint": "", "options": {}, "choices": []}]
0.47
numeric
tra_02016
[{"role": "user", "question": "<image>Find $y$.", "hint": "", "options": {}, "choices": []}]
11
numeric
tra_02017
[{"role": "user", "question": "<image>In $\\odot O, \\overline{E C}$ and $\\overline{A B}$ are diameters, and $\\angle B O D \\cong \\angle D O E \\cong \\angle E O F \\cong \\angle F O A$\r\nFind $m\\widehat{B C}$", "hint": "", "options": {}, "choices": []}]
90
numeric
tra_02018
[{"role": "user", "question": "<image>Find the value of $h$.", "hint": "", "options": {}, "choices": []}]
84.85
numeric
tra_02019
[{"role": "user", "question": "<image>Find the measure of the altitude drawn to the hypotenuse.", "hint": "", "options": {}, "choices": []}]
\sqrt { 612 }
open
tra_02020
[{"role": "user", "question": "<image>Find y.", "hint": "", "options": {}, "choices": []}]
7
numeric
tra_02021
[{"role": "user", "question": "<image>Find x", "hint": "", "options": {}, "choices": []}]
22
numeric
tra_02022
[{"role": "user", "question": "<image>Find the variable of $d$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "hint": "", "options": {}, "choices": []}]
16.9
numeric
tra_02023
[{"role": "user", "question": "<image>Find $x$.", "hint": "", "options": {}, "choices": []}]
28
numeric
tra_02024
[{"role": "user", "question": "<image>Find the area of the shaded sector. Round to the nearest tenth, if necessary.", "hint": "", "options": {}, "choices": []}]
167.1
numeric
tra_02025
[{"role": "user", "question": "<image>Find the length of $FG$", "hint": "", "options": {}, "choices": []}]
39
numeric
tra_02026
[{"role": "user", "question": "<image>In the figure, $\\overline{A B} \\parallel \\overline{C E} .$ If $D A=6,$ what is $D B ?$", "hint": "", "options": {}, "choices": []}]
6
numeric
tra_02027
[{"role": "user", "question": "<image>In the figure, $QR \\| TS$, $QT \\| RS$, and $m \\angle 1=131$. Find the measure of $\\angle 2$. ", "hint": "", "options": {}, "choices": []}]
49
numeric
tra_02028
[{"role": "user", "question": "<image>The area of a circle is 20 $\\pi$ square centimeters. What is its circumference?", "hint": "", "options": {}, "choices": []}]
4 \sqrt 5 \pi
open
tra_02029
[{"role": "user", "question": "<image>Find x", "hint": "", "options": {}, "choices": []}]
45
numeric
tra_02030
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
6
numeric
tra_02031
[{"role": "user", "question": "<image>Rhombus $A B C D$ is circumscribed about $\\odot P$ and has a perimeter of 32 Find $x$", "hint": "", "options": {}, "choices": []}]
5
numeric
tra_02032
[{"role": "user", "question": "<image>Find the area of the figure in feet. Round to the nearest tenth, if necessary.", "hint": "", "options": {}, "choices": []}]
31.2
numeric
tra_02033
[{"role": "user", "question": "<image>Find $m \\angle MNP$.", "hint": "", "options": {}, "choices": []}]
130
numeric
tra_02034
[{"role": "user", "question": "<image>In $\\odot S$, find $PR$.", "hint": "", "options": {}, "choices": []}]
12
numeric
tra_02035
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
12
numeric
tra_02036
[{"role": "user", "question": "<image>Refer to the triangle shown below. Find $z$ to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
\frac { 5 } { 2 } \sqrt { 41 }
open
tra_02037
[{"role": "user", "question": "<image>In $\\triangle EFG, \\overline{HL} \\parallel \\overline{EF}, EH=9, HG=21,$ and $FL=6 .$ Find $LG$", "hint": "", "options": {}, "choices": []}]
14
numeric
tra_02038
[{"role": "user", "question": "<image>Find $x$.", "hint": "", "options": {}, "choices": []}]
3
numeric
tra_02039
[{"role": "user", "question": "<image>Quadrilateral $ABDC$ is a rectangle. Find $m \\angle 6$ if $ m\\angle 1 = 38$.", "hint": "", "options": {}, "choices": []}]
38
numeric
tra_02040
[{"role": "user", "question": "<image>Find the area of the kite.", "hint": "", "options": {}, "choices": []}]
52.5
numeric
tra_02041
[{"role": "user", "question": "<image>In the figure, $ \\overline{GK} \\cong \\overline{GH}$ and $ \\overline{HK} \\cong \\overline{KJ}$. If $m \\angle HGK=28$, find $m \\angle HJK$.", "hint": "", "options": {}, "choices": []}]
38
numeric
tra_02042
[{"role": "user", "question": "<image>Find AS", "hint": "", "options": {}, "choices": []}]
8
numeric
tra_02043
[{"role": "user", "question": "<image>Find x. Assume that any segment that appears to be tangent is tangent.", "hint": "", "options": {}, "choices": []}]
13
numeric
tra_02044
[{"role": "user", "question": "<image>Find y.", "hint": "", "options": {}, "choices": []}]
3 \sqrt { 5 }
open
tra_02045
[{"role": "user", "question": "<image>Find the exact circumference of each circle.", "hint": "", "options": {}, "choices": []}]
5 \pi
open
tra_02046
[{"role": "user", "question": "<image>Find $m \\angle 1$.", "hint": "", "options": {}, "choices": []}]
85
numeric
tra_02047
[{"role": "user", "question": "<image>The area $A$ of the shaded region is given. Find $x$. $A = 94$ in$^2$ .", "hint": "", "options": {}, "choices": []}]
55.0
numeric
tra_02048
[{"role": "user", "question": "<image>Find $x$ if $\\overline{PS}$ is a median of $\\triangle PQR$.", "hint": "", "options": {}, "choices": []}]
2
numeric
tra_02049
[{"role": "user", "question": "<image>The diameters of $\\odot A, \\odot B,$ and $\\odot C$ are $8$ inches, $18$ inches, and $11$ inches, respectively. Find $FG$.", "hint": "", "options": {}, "choices": []}]
14
numeric
tra_02050
[{"role": "user", "question": "<image>Find y.", "hint": "", "options": {}, "choices": []}]
\frac { 25 } { 14 }
open
tra_02051
[{"role": "user", "question": "<image>If $\\overline{K H}$ is parallel to $\\overline{JI}$, find the measure of $\\angle 2$", "hint": "", "options": {}, "choices": []}]
54
numeric
tra_02052
[{"role": "user", "question": "<image>If $\\overline{E B} \\parallel \\overline{D C},$ find $x$", "hint": "", "options": {}, "choices": []}]
9.5
numeric
tra_02053
[{"role": "user", "question": "<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "hint": "", "options": {}, "choices": []}]
13.7
numeric
tra_02054
[{"role": "user", "question": "<image>$\\triangle ABC \\cong \\triangle FGH$. Find $x$.", "hint": "", "options": {}, "choices": []}]
3
numeric
tra_02055
[{"role": "user", "question": "<image>Points $S$, $T$, and $U$ are the midpoints of $\\overline{DE}$, $\\overline{EF}$, and $\\overline{DF}$, respectively. Find $x$.", "hint": "", "options": {}, "choices": []}]
4
numeric
tra_02056
[{"role": "user", "question": "<image>Find $m \\angle DBA$.", "hint": "", "options": {}, "choices": []}]
17
numeric
tra_02057
[{"role": "user", "question": "<image>Circle $L$ has a radius of 32 centimeters. $\\overline{L H} \\perp \\overline{G J},$ and $G J=40$ centimeters. Find $L K$", "hint": "", "options": {}, "choices": []}]
\sqrt { 624 }
open
tra_02058
[{"role": "user", "question": "<image>$\\triangle RST \\cong \\triangle VUT$. What is the area of $\\triangle RST$?", "hint": "", "options": {}, "choices": []}]
300
numeric
tra_02059
[{"role": "user", "question": "<image>Find x. Assume that any segment that appears to be tangent is tangent.", "hint": "", "options": {}, "choices": []}]
8
numeric
tra_02060
[{"role": "user", "question": "<image>In the figure, $m∠4 = 104$, $m∠14 = 118$. Find the measure of $\\angle 9$.", "hint": "", "options": {}, "choices": []}]
62
numeric
tra_02061
[{"role": "user", "question": "<image>Find the area of the parallelogram.", "hint": "", "options": {}, "choices": []}]
318.7
numeric
tra_02062
[{"role": "user", "question": "<image>Find $m \\angle C$.", "hint": "", "options": {}, "choices": []}]
47
numeric
tra_02063
[{"role": "user", "question": "<image>Find x", "hint": "", "options": {}, "choices": []}]
4 \sqrt { 3 }
open
tra_02064
[{"role": "user", "question": "<image>$m∠4 = 32$. Find the measure of $\\angle 3$.", "hint": "", "options": {}, "choices": []}]
90
numeric
tra_02065
[{"role": "user", "question": "<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 $r$.", "hint": "", "options": {}, "choices": []}]
6
numeric
tra_02066
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
5 \sqrt { 3 }
open
tra_02067
[{"role": "user", "question": "<image>Find the measure of $RT$ of equilateral triangle $RST$ if $RS = x + 9$, $ST = 2x$, and $RT = 3x - 9$.", "hint": "", "options": {}, "choices": []}]
18
numeric
tra_02068
[{"role": "user", "question": "<image>Find $m \\angle 4$.", "hint": "", "options": {}, "choices": []}]
52
numeric
tra_02069
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
10
numeric
tra_02070
[{"role": "user", "question": "<image>Find the area of $▱EFGH$.", "hint": "", "options": {}, "choices": []}]
90
numeric
tra_02071
[{"role": "user", "question": "<image>For trapezoid $T R S V, M$ and $N$ are midpoints of the legs. If $V S=21$ and $T R=44,$ find $M N$", "hint": "", "options": {}, "choices": []}]
32.5
numeric
tra_02072
[{"role": "user", "question": "<image> $m \\widehat{G H}=78$ Find $m\\angle 2$", "hint": "", "options": {}, "choices": []}]
51
numeric
tra_02073
[{"role": "user", "question": "<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "hint": "", "options": {}, "choices": []}]
6
numeric
tra_02074
[{"role": "user", "question": "<image>Find $x$.", "hint": "", "options": {}, "choices": []}]
170
numeric
tra_02075
[{"role": "user", "question": "<image>For the pair of similar figures, find the area of the green figure.", "hint": "", "options": {}, "choices": []}]
24
numeric
tra_02076
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
5 \sqrt { 2 }
open
tra_02077
[{"role": "user", "question": "<image>Find the area of the quadrilateral.", "hint": "", "options": {}, "choices": []}]
240
numeric
tra_02078
[{"role": "user", "question": "<image>Find y.", "hint": "", "options": {}, "choices": []}]
10
numeric
tra_02079
[{"role": "user", "question": "<image>If $\\overline{GH} \\cong \\overline{HK}$, $\\overline{HJ} \\cong \\overline{YK}$, and $m \\angle GJK=100$, what is the measure of $\\angle HGK$ ?", "hint": "", "options": {}, "choices": []}]
20
numeric
tra_02080
[{"role": "user", "question": "<image>$ACDF \\sim VWYZ$. Find $x$.", "hint": "", "options": {}, "choices": []}]
15
numeric
tra_02081
[{"role": "user", "question": "<image>Find the angle measure of $\\angle 2$.", "hint": "", "options": {}, "choices": []}]
128
numeric
tra_02082
[{"role": "user", "question": "<image>ABCD is a rhombus. If EB = 9, AB = 12 and $m\\angle ABD = 55$ . Find CE", "hint": "", "options": {}, "choices": []}]
\sqrt { 63 }
open
tra_02083
[{"role": "user", "question": "<image>Find the measure of $\\angle 3$.", "hint": "", "options": {}, "choices": []}]
14
numeric
tra_02084
[{"role": "user", "question": "<image>Find the area of the shaded sector. Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
46.5
numeric
tra_02085
[{"role": "user", "question": "<image>$\\overline{PQ}$ is tangent to circles $R$ and $S$. Find $PQ$.", "hint": "", "options": {}, "choices": []}]
4 \sqrt 6
open
tra_02086
[{"role": "user", "question": "<image>If $SP=4, PT=6$, and $QR=12$, find $SQ$.", "hint": "", "options": {}, "choices": []}]
8
numeric
tra_02087
[{"role": "user", "question": "<image>If $\\overline{PQ} \\cong \\overline{UQ}$ and $ m ∠ P = 32 $, find $ m ∠PUQ $.", "hint": "", "options": {}, "choices": []}]
32
numeric
tra_02088
[{"role": "user", "question": "<image>If CDFG is a kite, find GF", "hint": "", "options": {}, "choices": []}]
5
numeric
tra_02089
[{"role": "user", "question": "<image>Find $\\angle1$", "hint": "", "options": {}, "choices": []}]
112
numeric
tra_02090
[{"role": "user", "question": "<image>If $x=7 \\sqrt{3},$ find $y$", "hint": "", "options": {}, "choices": []}]
21 \sqrt { 3 }
open
tra_02091
[{"role": "user", "question": "<image>Find the variable of $r$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "hint": "", "options": {}, "choices": []}]
1.8
numeric
tra_02092
[{"role": "user", "question": "<image>Find $m \\angle DH$.", "hint": "", "options": {}, "choices": []}]
162
numeric
tra_02093
[{"role": "user", "question": "<image>Find $m \\angle 4$.", "hint": "", "options": {}, "choices": []}]
64
numeric
tra_02094
[{"role": "user", "question": "<image>Quadrilateral MNOP is a rhombus. If $m\\angle PON = 124$, find $m\\angle POM$.", "hint": "", "options": {}, "choices": []}]
62
numeric
tra_02095
[{"role": "user", "question": "<image>Find the area of the figure. Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
3.5
numeric
tra_02096
[{"role": "user", "question": "<image>$\\overline{PM}$ is a diameter of $\\odot R$. Find $m \\widehat {MNP}$.", "hint": "", "options": {}, "choices": []}]
180
numeric
tra_02097
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
15.5
numeric
tra_02098
[{"role": "user", "question": "<image>Find y in the figure.", "hint": "", "options": {}, "choices": []}]
5
numeric
tra_02099
[{"role": "user", "question": "<image>For the pair of similar figures, use the given areas to find $x$.", "hint": "", "options": {}, "choices": []}]
10.0
numeric