Datasets:
mm-eval
/
Geometry3K

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34
question_type
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2 values
tra_01100
[{"role": "user", "question": "<image>Find the area of the trapezoid.", "hint": "", "options": {}, "choices": []}]
273
numeric
tra_01101
[{"role": "user", "question": "<image>Refer to trapezoid $CDFG$ with median $\\overline{HE}$. Let $\\overline{YZ}$ be the median of $HEFG$. Find $YZ$.", "hint": "", "options": {}, "choices": []}]
34
numeric
tra_01102
[{"role": "user", "question": "<image>Use the figure to find the indicated variable. If $m \\angle 4 = 2x - 17$ and $m \\angle 1 = 85$, find $x$.", "hint": "", "options": {}, "choices": []}]
56
numeric
tra_01103
[{"role": "user", "question": "<image>If $m∠2 = 4x + 7$ and $m∠7 = 5x - 13$, find $x$.", "hint": "", "options": {}, "choices": []}]
20
numeric
tra_01104
[{"role": "user", "question": "<image>Find the value of x.", "hint": "", "options": {}, "choices": []}]
45
numeric
tra_01105
[{"role": "user", "question": "<image>$m \\widehat{J H}=114$ Find $m\\angle 3$", "hint": "", "options": {}, "choices": []}]
33
numeric
tra_01106
[{"role": "user", "question": "<image>Find x. Round to the nearest tenth if necessary.", "hint": "", "options": {}, "choices": []}]
2
numeric
tra_01107
[{"role": "user", "question": "<image>In the figure, $LH$ is the midsegment of trapezoid $FGJK$. What is the value of $x$ ?", "hint": "", "options": {}, "choices": []}]
11.8
numeric
tra_01108
[{"role": "user", "question": "<image>Find the area of the shaded region.", "hint": "", "options": {}, "choices": []}]
50.3
numeric
tra_01109
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
\sqrt { 141 }
open
tra_01110
[{"role": "user", "question": "<image>Find the perimeter or circumference of the figure. Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
16
numeric
tra_01111
[{"role": "user", "question": "<image>Find $x$.", "hint": "", "options": {}, "choices": []}]
10
numeric
tra_01112
[{"role": "user", "question": "<image>Refer to the figure at the right. Find the value of $m ∠BCE$ if $ p \\parallel q $.", "hint": "", "options": {}, "choices": []}]
75
numeric
tra_01113
[{"role": "user", "question": "<image>Find the area of the shaded region. Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
37.4
numeric
tra_01114
[{"role": "user", "question": "<image>Find the perimeter of $▱ JKLM$.", "hint": "", "options": {}, "choices": []}]
22.4
numeric
tra_01115
[{"role": "user", "question": "<image>find sin A", "hint": "", "options": {}, "choices": []}]
\frac { 5 } { 7 }
open
tra_01116
[{"role": "user", "question": "<image>Find the measure of $∠T$ to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
56.4
numeric
tra_01117
[{"role": "user", "question": "<image>Find the perimeter of the parallelogram.", "hint": "", "options": {}, "choices": []}]
76
numeric
tra_01118
[{"role": "user", "question": "<image>Find the measure of $∠R$ to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
39.6
numeric
tra_01119
[{"role": "user", "question": "<image>$\\triangle MHJ \\cong \\triangle PQJ$. Find $y$.", "hint": "", "options": {}, "choices": []}]
5
numeric
tra_01120
[{"role": "user", "question": "<image>In $\\triangle ACE$, $P$ is the centroid. $PF=6$ and $AD=15$. Find $AP$.", "hint": "", "options": {}, "choices": []}]
10
numeric
tra_01121
[{"role": "user", "question": "<image>Find the area of the figure. Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
374
numeric
tra_01122
[{"role": "user", "question": "<image>Find z ", "hint": "", "options": {}, "choices": []}]
4 \sqrt { 3 }
open
tra_01123
[{"role": "user", "question": "<image>In the figure, $m∠1 = 50$ and $m∠3 = 60$. Find the measure of $\\angle 5$.", "hint": "", "options": {}, "choices": []}]
60
numeric
tra_01124
[{"role": "user", "question": "<image>Find x", "hint": "", "options": {}, "choices": []}]
41.8
numeric
tra_01125
[{"role": "user", "question": "<image>Use parallelogram ABCD to find $y $", "hint": "", "options": {}, "choices": []}]
11
numeric
tra_01126
[{"role": "user", "question": "<image>Find the value of $d$ in the parallelogram", "hint": "", "options": {}, "choices": []}]
42
numeric
tra_01127
[{"role": "user", "question": "<image>Find y.", "hint": "", "options": {}, "choices": []}]
15
numeric
tra_01128
[{"role": "user", "question": "<image>Solve for $x$.", "hint": "", "options": {}, "choices": []}]
12
numeric
tra_01129
[{"role": "user", "question": "<image>In the figure, $m∠3 = 43$. Find the measure of $\\angle 13$.", "hint": "", "options": {}, "choices": []}]
43
numeric
tra_01130
[{"role": "user", "question": "<image>Find x", "hint": "", "options": {}, "choices": []}]
35
numeric
tra_01131
[{"role": "user", "question": "<image>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 $m \\angle PXR=2 a+10$. Find $PR$ if $\\overline{QY}$ is a median.", "hint": "", "options": {}, "choices": []}]
18
numeric
tra_01132
[{"role": "user", "question": "<image>Find the area of the shaded region. Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
66.3
numeric
tra_01133
[{"role": "user", "question": "<image>What is the circumference of $\\odot T$? Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
40.8
numeric
tra_01134
[{"role": "user", "question": "<image>Use parallelogram to find $a$", "hint": "", "options": {}, "choices": []}]
7
numeric
tra_01135
[{"role": "user", "question": "<image>In $\\odot F, \\overline{F H} \\cong \\overline{F L}$ and $\\mathrm{FK}=17$.\r\nFind LK", "hint": "", "options": {}, "choices": []}]
15
numeric
tra_01136
[{"role": "user", "question": "<image>In the figure, $\\triangle FGH$ is a right triangle with hypotenuse $\\overline{FH}$ and $GJ = GH$. What is the measure of $∠JGH$?", "hint": "", "options": {}, "choices": []}]
56
numeric
tra_01137
[{"role": "user", "question": "<image>The area of trapezoid $JKLM$ is 138 square feet. The area of trapezoid $QRST$ is 5.52 square feet. If trapezoid $J K L M$ $ \\sim$ trapezoid $QRST$, find the scale factor from trapezoid $JKLM$ to trapezoid $QRST$.", "hint": "", "options": {}, "choices": []}]
5
numeric
tra_01138
[{"role": "user", "question": "<image>If $A D=8, A E=12,$ and $E C=18,$ find $A B$", "hint": "", "options": {}, "choices": []}]
20
numeric
tra_01139
[{"role": "user", "question": "<image>Find the area of the shaded region. Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
53.5
numeric
tra_01140
[{"role": "user", "question": "<image>Find $x$.", "hint": "", "options": {}, "choices": []}]
6
numeric
tra_01141
[{"role": "user", "question": "<image>Find $x$ in $\\triangle P Q R$", "hint": "", "options": {}, "choices": []}]
2 \sqrt { 6 }
open
tra_01142
[{"role": "user", "question": "<image>Find the length of $AB$ in the isosceles triangle $ABC$. ", "hint": "", "options": {}, "choices": []}]
12.5
numeric
tra_01143
[{"role": "user", "question": "<image>Find the measure of $\\angle 3$.", "hint": "", "options": {}, "choices": []}]
147
numeric
tra_01144
[{"role": "user", "question": "<image>Find $m \\widehat{JK}$.", "hint": "", "options": {}, "choices": []}]
56
numeric
tra_01145
[{"role": "user", "question": "<image>Use rectangle LMNP, parallelogram LKMJ to solve the problem.\r\nIf $m \\angle P L K=110,$ find $m \\angle L K M$", "hint": "", "options": {}, "choices": []}]
140
numeric
tra_01146
[{"role": "user", "question": "<image>The segment is tangent to the circle. Find $x$.", "hint": "", "options": {}, "choices": []}]
8
numeric
tra_01147
[{"role": "user", "question": "<image>Chords $\\overline{JF}$ and $\\overline{BC}$ intersect at $K .$ If $B K=8$, $K C=12,$ and $K F=16,$ find $J K$", "hint": "", "options": {}, "choices": []}]
6
numeric
tra_01148
[{"role": "user", "question": "<image>find tan A", "hint": "", "options": {}, "choices": []}]
\frac { 15 } { 16 }
open
tra_01149
[{"role": "user", "question": "<image>Use parallelogram PQRS to find $QR$", "hint": "", "options": {}, "choices": []}]
3
numeric
tra_01150
[{"role": "user", "question": "<image>RSTV is a trapezoid with bases $\\overline{R V}$ and $\\overline{S T}$ and median $\\overline{M N}$. Find $x$ if $M N=60, S T=4 x-1,$ and $R V=6 x+11$", "hint": "", "options": {}, "choices": []}]
11
numeric
tra_01151
[{"role": "user", "question": "<image>In $\\odot F$, $GK=14$ and $m \\widehat{GHK}=142$. Find $m \\widehat {GH}$.", "hint": "", "options": {}, "choices": []}]
71
numeric
tra_01152
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
8 \sqrt { 3 }
open
tra_01153
[{"role": "user", "question": "<image>Each pair of polygons is similar. Find x.", "hint": "", "options": {}, "choices": []}]
91
numeric
tra_01154
[{"role": "user", "question": "<image>Find $x$ in each figure.", "hint": "", "options": {}, "choices": []}]
13
numeric
tra_01155
[{"role": "user", "question": "<image>Find the area of the rhombus.", "hint": "", "options": {}, "choices": []}]
60
numeric
tra_01156
[{"role": "user", "question": "<image>Find y.", "hint": "", "options": {}, "choices": []}]
20
numeric
tra_01157
[{"role": "user", "question": "<image>Find $m \\angle 4$.", "hint": "", "options": {}, "choices": []}]
40
numeric
tra_01158
[{"role": "user", "question": "<image>Quadrilateral ABCD is a rhombus. If $m\\angle BCD = 120$, find $m\\angle DAC$.", "hint": "", "options": {}, "choices": []}]
60
numeric
tra_01159
[{"role": "user", "question": "<image>Find $y$ so that $\\overline{BE}$ and $\\overline{AD}$ are perpendicular.", "hint": "", "options": {}, "choices": []}]
8.3
numeric
tra_01160
[{"role": "user", "question": "<image>Find the area of the figure. Round to the nearest tenth if necessary.", "hint": "", "options": {}, "choices": []}]
80
numeric
tra_01161
[{"role": "user", "question": "<image>If $A N$ is 5 meters long, find the exact circumference of $\\odot N .$", "hint": "", "options": {}, "choices": []}]
10 \pi
open
tra_01162
[{"role": "user", "question": "<image>In the figure, $m∠1 = 94$. Find the measure of $\\angle 3$.", "hint": "", "options": {}, "choices": []}]
94
numeric
tra_01163
[{"role": "user", "question": "<image>In the figure, $QR \\| TS$, $QT \\| RS$, and $m \\angle 1=131$. Find the measure of $\\angle 4$. ", "hint": "", "options": {}, "choices": []}]
49
numeric
tra_01164
[{"role": "user", "question": "<image>Circle $O$ has a radius of $10, A B=10$ and $m \\overrightarrow{A B}=60 .$ Find $m\\widehat{O X}$", "hint": "", "options": {}, "choices": []}]
5 \sqrt { 3 }
open
tra_01165
[{"role": "user", "question": "<image>Each pair of polygons is similar. Find y.", "hint": "", "options": {}, "choices": []}]
30
numeric
tra_01166
[{"role": "user", "question": "<image>Find x", "hint": "", "options": {}, "choices": []}]
8 \sqrt { 41 }
open
tra_01167
[{"role": "user", "question": "<image>Express the ratio of $\\tan A$ as a decimal to the nearest hundredth.", "hint": "", "options": {}, "choices": []}]
1.33
numeric
tra_01168
[{"role": "user", "question": "<image>In A, the radius is $14$ and $CD = 22$. Find $EB$. Round to the nearest hundredth.", "hint": "", "options": {}, "choices": []}]
5.34
numeric
tra_01169
[{"role": "user", "question": "<image>Find $x$.", "hint": "", "options": {}, "choices": []}]
70
numeric
tra_01170
[{"role": "user", "question": "<image>$\\overline{HK}$ and $\\overline{IG}$ are diameters of $\\odot L$. Find $m \\widehat {HGK}$.", "hint": "", "options": {}, "choices": []}]
180
numeric
tra_01171
[{"role": "user", "question": "<image>If $\\angle R S T$ is a right angle, $\\overline{SU} \\perp \\overline{RT}$, $\\overline{UV} \\perp \\overline{ST},$ and $m \\angle RT S=47,$ find $m \\angle R$", "hint": "", "options": {}, "choices": []}]
43
numeric
tra_01172
[{"role": "user", "question": "<image>Find $x$ if $\\overline{AD}$ is a median of $\\triangle ABC$.", "hint": "", "options": {}, "choices": []}]
5
numeric
tra_01173
[{"role": "user", "question": "<image>Use parallelogram MNPR to find $y$", "hint": "", "options": {}, "choices": []}]
6.45
numeric
tra_01174
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
6 \sqrt { 3 }
open
tra_01175
[{"role": "user", "question": "<image>Find the area of the figure. Round to the nearest tenth, if necessary.", "hint": "", "options": {}, "choices": []}]
1050
numeric
tra_01176
[{"role": "user", "question": "<image>Find the perimeter of $\\triangle P Q R,$ if $\\triangle P Q M \\sim \\triangle P R Q$\r\n", "hint": "", "options": {}, "choices": []}]
78
numeric
tra_01177
[{"role": "user", "question": "<image>Find the circumference of the figure. Round to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
18.8
numeric
tra_01178
[{"role": "user", "question": "<image>Find x.", "hint": "", "options": {}, "choices": []}]
35
numeric
tra_01179
[{"role": "user", "question": "<image>Find $x$. $A = 92$ in$^2$.", "hint": "", "options": {}, "choices": []}]
8.4
numeric
tra_01180
[{"role": "user", "question": "<image>The diameter of $\\odot S$ is $30$ units, the diameter of $\\odot R$ is $20$ units, and $DS=9$ units. Find $CD$.", "hint": "", "options": {}, "choices": []}]
6
numeric
tra_01181
[{"role": "user", "question": "<image>In the figure, $m ∠1 = 53$. Find the measure of $∠5$.", "hint": "", "options": {}, "choices": []}]
127
numeric
tra_01182
[{"role": "user", "question": "<image>In the figure, $QR \\| TS$, $QT \\| RS$, and $m \\angle 1=131$. Find the measure of $\\angle 8$. ", "hint": "", "options": {}, "choices": []}]
131
numeric
tra_01183
[{"role": "user", "question": "<image>Find the perimeter of the figure. Round to the nearest hundredth, if necessary.", "hint": "", "options": {}, "choices": []}]
37.9
numeric
tra_01184
[{"role": "user", "question": "<image>Find the area of the kite.", "hint": "", "options": {}, "choices": []}]
60
numeric
tra_01185
[{"role": "user", "question": "<image>Find $m\\angle 1$.", "hint": "", "options": {}, "choices": []}]
59
numeric
tra_01186
[{"role": "user", "question": "<image>Express the ratio of $\\tan V$ as a decimal to the nearest hundredth.", "hint": "", "options": {}, "choices": []}]
0.29
numeric
tra_01187
[{"role": "user", "question": "<image>For trapezoid QRTU, V and S are midpoints of the legs. If VS = 9 and UT = 12, find QR.", "hint": "", "options": {}, "choices": []}]
7
numeric
tra_01188
[{"role": "user", "question": "<image>Find $m\\angle Q$", "hint": "", "options": {}, "choices": []}]
121
numeric
tra_01189
[{"role": "user", "question": "<image>Refer to the triangle shown below. Find $x$ to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
10
numeric
tra_01190
[{"role": "user", "question": "<image>$a=14, b=48,$ and $c=50$, find $sinB$", "hint": "", "options": {}, "choices": []}]
0.96
numeric
tra_01191
[{"role": "user", "question": "<image>Find the area of the figure. Round to the nearest tenth if necessary.", "hint": "", "options": {}, "choices": []}]
155.5
numeric
tra_01192
[{"role": "user", "question": "<image>Find QX if $E X=24$ and $D E=7$", "hint": "", "options": {}, "choices": []}]
18
numeric
tra_01193
[{"role": "user", "question": "<image>Find $x$. $A = 104$ ft$^2$.", "hint": "", "options": {}, "choices": []}]
6.3
numeric
tra_01194
[{"role": "user", "question": "<image>Find y.", "hint": "", "options": {}, "choices": []}]
10
numeric
tra_01195
[{"role": "user", "question": "<image>Find $x$. (Hint: Draw an auxiliary line.)", "hint": "", "options": {}, "choices": []}]
22
numeric
tra_01196
[{"role": "user", "question": "<image>Find x to the nearest tenth.", "hint": "", "options": {}, "choices": []}]
9.67
numeric
tra_01197
[{"role": "user", "question": "<image>In $\\odot A, m \\angle E A D=42$. Find $m \\widehat{C B E}$", "hint": "", "options": {}, "choices": []}]
180
numeric
tra_01198
[{"role": "user", "question": "<image>Use parallelogram JKLM to find $a$ if $J K=2 b+3$ and $J M=3 a$.", "hint": "", "options": {}, "choices": []}]
7
numeric
tra_01199
[{"role": "user", "question": "<image>Find $x$.", "hint": "", "options": {}, "choices": []}]
45
numeric