OpenVLThinker-v1.2 Datasets
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problem
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<image>If DE = 60 and FC = 16, find the length of segment AC
|
62
|
geometry3k
|
data/llavaone/identity_81733.jpg
| |
<image>If a = 10 \sqrt { 3 }, find C E.
Choices:
(A) 5 \sqrt 3
(B) 10
(C) 15
(D) 10 \sqrt 3
|
c
|
geometry3k
|
data/llavaone/identity_9658.jpg
| |
<image>If the figure is cut along the dashed line, what is the area of one of the resulting triangles?
|
97.5
|
geometry3k
|
data/llavaone/identity_161279.jpg
| |
<image>What is the measure of angle QRP in the parallelogram M N P R?
|
83
|
geometry3k
|
data/llavaone/identity_91122.jpg
| |
<image>What is the measure of angle 4?
|
49
|
geometry3k
|
data/llavaone/identity_89980.jpg
| |
<image>What is the perimeter of triangle JKL?
|
27.5
|
geometry3k
|
data/llavaone/identity_83461.jpg
| |
<image>What is the measure of angle J in the given pentagon EFGHJ?
|
112°
|
geometry3k
|
data/llavaone/identity_81189.jpg
| |
<image>What is the measure of angle 8 in the rectangle ABCD?
|
90
|
geometry3k
|
data/llavaone/identity_80060.jpg
| |
<image>In quadrilateral ABCD inscribed in circle Z, angle BZA measures 104 degrees, angle CBA measures 94 degrees, and AB is parallel to DC. What is the measure of angle BZA?
Choices:
(A) 36
(B) 90
(C) 104
(D) 120
|
c
|
geometry3k
|
data/llavaone/identity_278854.jpg
| |
<image>Find G H.
Choices:
(A) 17
(B) 35
(C) 39
(D) 45
|
c
|
geometry3k
|
data/llavaone/identity_12705.jpg
| |
<image>m \angle 11 = 4 x, m \angle 12 = 2 x - 6. Find the measure of \angle 11.
Choices:
(A) 116
(B) 118
(C) 120
(D) 124
|
d
|
geometry3k
|
data/llavaone/identity_11773.jpg
| |
<image>What is the measure of angle 2, the angle adjacent to angle 1?
|
54
|
geometry3k
|
data/llavaone/identity_80529.jpg
| |
<image>What is the length of segment HJ?
|
8.1
|
geometry3k
|
data/llavaone/identity_89701.jpg
| |
<image>What is the measure of angle ACB in the triangle ABC?
|
25.5
|
geometry3k
|
data/llavaone/identity_90660.jpg
| |
<image>A B is tangent to the circle. Determine the value of x. Round to the nearest tenth.
Choices:
(A) 5.1
(B) 6.1
(C) 7.1
(D) 8.1
|
b
|
geometry3k
|
data/llavaone/identity_330693.jpg
| |
<image>E D is tangent to \odot F at point E. Find x.
Choices:
(A) 3
(B) 4
(C) 5
(D) 6
|
c
|
geometry3k
|
data/llavaone/identity_10350.jpg
| |
<image>If angle y were to increase by 10 degrees, what would be the new value of angle z?
|
44
|
geometry3k
|
data/llavaone/identity_87597.jpg
| |
<image>Determine the scale factor from W to W' among the given choices: (A) 0.75, (B) 1.25, (C) 1.5, (D) 1.75.
|
a
|
geometry3k
|
data/llavaone/identity_277988.jpg
| |
<image>What is the measure of angle AOB?
|
180
|
geometry3k
|
data/llavaone/identity_89782.jpg
| |
<image>Determine the measure of angle K.
Choices:
(A) 62
(B) 72
(C) 116
(D) 160
|
a
|
geometry3k
|
data/llavaone/identity_301710.jpg
| |
<image>What is the length of side y?
|
11.16
|
geometry3k
|
data/llavaone/identity_161749.jpg
| |
<image>a = 14, b = 48, and c = 50, find \tan B.
Choices:
(A) 3.43
(B) 4.8
(C) 5.2
(D) 6.86
|
a
|
geometry3k
|
data/llavaone/identity_2811.jpg
| |
<image>Given rhombus XYZW with m∠WYZ = 53°, VW = 3, XV = 2a - 2, and ZV = (5a + 1)/4, find the length of diagonal XZ
|
9.48
|
geometry3k
|
data/llavaone/identity_84766.jpg
| |
<image>Determine the measure of angle 1.
Options:
(A) 31
(B) 42
(C) 59
(D) 63
|
c
|
geometry3k
|
data/llavaone/identity_279090.jpg
| |
<image>Given that the pairs of triangles are similar, find the length of side \( QS \) in triangle \( QRS \)
|
8
|
geometry3k
|
data/llavaone/identity_232682.jpg
| |
<image>If line m is rotated 45° clockwise, what is the new measure of the angle between the transversal and line m?
|
45°
|
geometry3k
|
data/llavaone/identity_161739.jpg
| |
<image>Find the value of x in triangle HJK
|
3/4
|
geometry3k
|
data/llavaone/identity_84510.jpg
| |
<image>What is the measure of the central angle corresponding to the arc marked as 150 degrees?
|
150
|
geometry3k
|
data/llavaone/identity_89391.jpg
| |
<image>Find the measure of angle 1
|
16
|
geometry3k
|
data/llavaone/identity_231026.jpg
| |
<image>What is the length of side JN in triangle JMN?
|
2
|
geometry3k
|
data/llavaone/identity_81175.jpg
| |
<image>What is the value of x when y equals 15?
|
9/5
|
geometry3k
|
data/llavaone/identity_80475.jpg
| |
<image>Given that the diameters of circles A, B, and C are 8 inches, 18 inches, and 11 inches, respectively, what is the diameter of circle B?
(A) 4
(B) 5
(C) 5.5
(D) 11
|
b
|
geometry3k
|
data/llavaone/identity_262546.jpg
| |
<image>What is the ratio of the areas of triangle QRS to triangle QTP?
|
0.474609375
|
geometry3k
|
data/llavaone/identity_80735.jpg
| |
<image>Given m \widehat F E = 118, m \widehat A B = 108, m \angle E G B = 52, and m \angle E F B = 30, find the measure of angle DAB
|
67
|
geometry3k
|
data/llavaone/identity_241597.jpg
| |
<image>Find the measure of \(\angle 3\) in the figure
|
5
|
geometry3k
|
data/llavaone/identity_234489.jpg
| |
<image>If XM = 4, XN = 6, and NZ = 9, find the length of YZ
|
10
|
geometry3k
|
data/llavaone/identity_159743.jpg
| |
<image>Use parallelogram J K L M to find m \angle M J K.
Choices:
(A) 80
(B) 100
(C) 110
(D) 120
|
b
|
geometry3k
|
data/llavaone/identity_17365.jpg
| |
<image>Determine the measure of \(\angle 6\) given that \(l \parallel m\) and \(\angle 1 = 105^\circ\).
Choices:
(A) 75
(B) 85
(C) 95
(D) 105
|
d
|
geometry3k
|
data/llavaone/identity_305466.jpg
| |
<image>What is the length of the shorter side of the parallelogram?
|
8
|
geometry3k
|
data/llavaone/identity_82514.jpg
| |
<image>What is the measure of angle 3?
Choices:
(A) 65
(B) 70
(C) 95
(D) 110
|
c
|
geometry3k
|
data/llavaone/identity_262006.jpg
| |
<image>What is the measure of \angle 1?
|
109
|
geometry3k
|
data/llavaone/identity_79578.jpg
| |
<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary
|
126 ft
|
geometry3k
|
data/llavaone/identity_243658.jpg
| |
<image>If triangle JKL is similar to triangle WYZ, find the value of x
|
19.5
|
geometry3k
|
data/llavaone/identity_87140.jpg
| |
<image>What is the value of x in the parallelogram NQRM?
|
4
|
geometry3k
|
data/llavaone/identity_78935.jpg
| |
<image>Find x.
Choices:
(A) 6
(B) 8
(C) 10
(D) 12
|
a
|
geometry3k
|
data/llavaone/identity_18297.jpg
| |
<image>Find the measure of angle KMN
|
140
|
geometry3k
|
data/llavaone/identity_90398.jpg
| |
<image>If JKLM is a rectangle and the diagonals intersect at point P, what is the measure of angle JPK?
|
45
|
geometry3k
|
data/llavaone/identity_163315.jpg
| |
<image>What is the measure of the angle formed by the tangent and the chord at the point of tangency?
|
5x°
|
geometry3k
|
data/llavaone/identity_79649.jpg
| |
<image>What is the measure of angle 4?
|
53
|
geometry3k
|
data/llavaone/identity_90673.jpg
| |
<image>What is the circumference of the entire circle?
|
8.17
|
geometry3k
|
data/llavaone/identity_81068.jpg
| |
<image>Given that J M is congruent to P M and M L is congruent to P L in the figure, and the measure of angle P L J is 34 degrees, what is the measure of angle J P M?
Choices:
(A) 34
(B) 34.5
(C) 36
(D) 36.5
|
d
|
geometry3k
|
data/llavaone/identity_262569.jpg
| |
<image>In triangle JLP, if JK = 3y - 2 and LK = 5y - 8, find the value of y when JK = LK
|
3
|
geometry3k
|
data/llavaone/identity_161741.jpg
| |
<image>Determine the value of x.
Options:
(A) 7
(B) 8
(C) 11
(D) 13
|
b
|
geometry3k
|
data/llavaone/identity_303371.jpg
| |
<image>What is the sum of the measures of the angles at one pair of opposite vertices in the parallelogram?
|
161°
|
geometry3k
|
data/llavaone/identity_84951.jpg
| |
<image>Find the area of the shaded region if the radius of the circle is 10 units and the square is inscribed in the circle. Round to the nearest tenth
|
114
|
geometry3k
|
data/llavaone/identity_255407.jpg
| |
<image>Given that UJ = 9, VJ = 3, and ZT = 18, find the perimeter of triangle ZJT
|
33
|
geometry3k
|
data/llavaone/identity_240022.jpg
| |
<image>If the length of WY is 10 units, what is the length of XZ?
|
20 units
|
geometry3k
|
data/llavaone/identity_88872.jpg
| |
<image>What is the area of the triangle?
|
37.5√3
|
geometry3k
|
data/llavaone/identity_160076.jpg
| |
<image>What is the length of the radius of the circle?
|
3.5
|
geometry3k
|
data/llavaone/identity_79038.jpg
| |
<image>What is the perimeter of triangle ABC?
|
59
|
geometry3k
|
data/llavaone/identity_85705.jpg
| |
<image>What is the length of side MN in the parallelogram M N P R?
|
28.3
|
geometry3k
|
data/llavaone/identity_91120.jpg
| |
<image>What is the perimeter of the right triangle if x equals 6?
|
32
|
geometry3k
|
data/llavaone/identity_85018.jpg
| |
<image>If the polygon shown is regular, what is the measure of angle ABC?
Choices:
(A) 140
(B) 144
(C) 162
(D) 180
|
a
|
geometry3k
|
data/llavaone/identity_306657.jpg
| |
<image>Given that the measure of angle 3 is 43 degrees in the figure, what is the measure of angle 7?
Choices:
(A) 43
(B) 53
(C) 127
(D) 137
|
a
|
geometry3k
|
data/llavaone/identity_262366.jpg
| |
<image>If another parallelogram is constructed with the same height but twice the base length, what would be its area?
|
2128 m^2
|
geometry3k
|
data/llavaone/identity_160514.jpg
| |
<image>What is the measure of angle 1 in the rectangle ABCD?
|
50
|
geometry3k
|
data/llavaone/identity_89741.jpg
| |
<image>Find the area of the entire circle and then determine the area of the shaded region, which is a sector of the circle with a central angle of 130 degrees. Round your final answer to the nearest tenth
|
10.2
|
geometry3k
|
data/llavaone/identity_225577.jpg
| |
<image>Find K L.
Choices:
(A) 3
(B) 6
(C) 12
(D) 18
|
b
|
geometry3k
|
data/llavaone/identity_27337.jpg
| |
<image>Given that triangle ABC is congruent to triangle FGH, find the length of side FH
|
19
|
geometry3k
|
data/llavaone/identity_90454.jpg
| |
<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.
Choices:
(A) 16.8
(B) 19.2
(C) 21.6
(D) 22.7
|
b
|
geometry3k
|
data/llavaone/identity_12872.jpg
| |
<image>If trapezoid ABCD is isosceles and the diagonals intersect at point P, what is the measure of angle APD?
|
180
|
geometry3k
|
data/llavaone/identity_165661.jpg
| |
<image>If the diameters of circle A are DF and PG, and AG is equal to 12, what is the length of LA?
Choices:
(A) 12
(B) 24
(C) 36
(D) 48
|
a
|
geometry3k
|
data/llavaone/identity_270416.jpg
| |
<image>What is the measure of the central angle of the circle?
|
110°
|
geometry3k
|
data/llavaone/identity_160360.jpg
| |
<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.
Choices:
(A) 3.2
(B) 6.4
(C) 12.8
(D) 16
|
c
|
geometry3k
|
data/llavaone/identity_37515.jpg
| |
<image>What is the measure of angle AFB?
|
139.9
|
geometry3k
|
data/llavaone/identity_88942.jpg
| |
<image>What is the measure of the angle JFH in the circle?
|
65°
|
geometry3k
|
data/llavaone/identity_165641.jpg
| |
<image>What is the measure of angle BFG in the circle?
|
90
|
geometry3k
|
data/llavaone/identity_89076.jpg
| |
<image>In \odot F, G K = 14 and m \widehat G H K = 142. Determine J K.
Choices:
(A) 7
(B) 8
(C) 14
(D) 16
|
a
|
geometry3k
|
data/llavaone/identity_323707.jpg
| |
<image>In the given figure, what is the value of x?
Options:
(A) 19
(B) 23
(C) 26
(D) 28
|
c
|
geometry3k
|
data/llavaone/identity_268469.jpg
| |
<image>In the diagram, m \angle 1 = 50 and m \angle 3 = 60. Determine the measure of \angle 5.
Choices:
(A) 50
(B) 60
(C) 70
(D) 80
|
b
|
geometry3k
|
data/llavaone/identity_305368.jpg
| |
<image>If UJ = 9, VJ = 3, and ZT = 18, find the length of segment ZU
|
33
|
geometry3k
|
data/llavaone/identity_83652.jpg
| |
<image>Find the measure of angle 1
|
62
|
geometry3k
|
data/llavaone/identity_159780.jpg
| |
<image>What is the measure of angle JMK?
|
90
|
geometry3k
|
data/llavaone/identity_83462.jpg
| |
<image>What is the measure of angle 4 in the figure?
|
50
|
geometry3k
|
data/llavaone/identity_91353.jpg
| |
<image>If the line with the 78° angle is a transversal intersecting two parallel lines, what is the measure of the angle directly opposite to the 78° angle on the other parallel line?
|
78°
|
geometry3k
|
data/llavaone/identity_159412.jpg
| |
<image>Determine the value of x.
Options:
(A) 3√5
(B) 4√5
(C) 5√5
(D) 6√5
|
a
|
geometry3k
|
data/llavaone/identity_282035.jpg
| |
<image>Determine the value of x.
Options:
(A) 4
(B) 4 \sqrt { 3 }
(C) 8
(D) 6 \sqrt { 3 }
|
a
|
geometry3k
|
data/llavaone/identity_269687.jpg
| |
<image>Given that quadrilateral ABCD is a rectangle, find the value of x
|
24.857
|
geometry3k
|
data/llavaone/identity_243982.jpg
| |
<image>If M N O P is a rhombus, what is the measure of angle MRP?
|
45°
|
geometry3k
|
data/llavaone/identity_89727.jpg
| |
<image>What is the diameter of the circle?
|
6
|
geometry3k
|
data/llavaone/identity_83300.jpg
| |
<image>In the diagram, m \angle 8 = 96 and m \angle 12 = 42. Determine the measure of \angle 9.
Options:
(A) 42
(B) 84
(C) 94
(D) 96
|
b
|
geometry3k
|
data/llavaone/identity_318885.jpg
| |
<image>If each arrow represents x degrees, what is the value of x?
|
30
|
geometry3k
|
data/llavaone/identity_80374.jpg
| |
<image>Polygon B C D E \cong polygon R S T U. Find z.
Choices:
(A) 3
(B) 10
(C) 20
(D) 42
|
a
|
geometry3k
|
data/llavaone/identity_18740.jpg
| |
<image>Find the measure of \angle 2
|
32°
|
geometry3k
|
data/llavaone/identity_81642.jpg
| |
<image>What is the area of the circle?
|
3π
|
geometry3k
|
data/llavaone/identity_84314.jpg
| |
<image>What is the sum of the interior angles of the quadrilateral?
|
360
|
geometry3k
|
data/llavaone/identity_84772.jpg
| |
<image>Given that MC = 7, RM = 4, and AT = 16, what is the value of SC?
(A) 10.5
(B) 12
(C) 13.5
(D) 21
|
a
|
geometry3k
|
data/llavaone/identity_278936.jpg
| |
<image>\triangle P Q S \cong \triangle R Q S. Find x.
Choices:
(A) 8
(B) 12
(C) 16
(D) 20
|
c
|
geometry3k
|
data/llavaone/identity_35187.jpg
| |
<image>Given that in the figure, the measure of angle 1 is 58 degrees, angle 2 is 47 degrees, and angle 3 is 26 degrees, what is the measure of angle 7?
Choices:
(A) 47
(B) 49
(C) 58
(D) 73
|
c
|
geometry3k
|
data/llavaone/identity_264352.jpg
| |
<image>In triangle ABC, H is the incenter. Determine the length of BD.
Choices:
(A) 7√3
(B) 7
(C) 7√3
(D) 14
|
c
|
geometry3k
|
data/llavaone/identity_263134.jpg
|
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