problem
stringlengths 7
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| images
images listlengths 1
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|---|---|---|---|---|
<image>What is the perimeter of the purple shaded region in the image?
|
50 + 6π
|
geometry3k
|
data/llavaone/identity_80486.jpg
| |
<image>If the quadrilateral is a parallelogram, what is the ratio of the length of the side labeled 2x + 3 to the side labeled 4y?
|
5:36
|
geometry3k
|
data/llavaone/identity_90787.jpg
| |
<image>If m \angle 1 = 50 and m \angle 3 = 60, find the measure of \angle 4
|
50
|
geometry3k
|
data/llavaone/identity_85188.jpg
| |
<image>What is the measure of angle RTM?
Choices:
(A) 54
(B) 63
(C) 108
(D) 126
|
d
|
geometry3k
|
data/llavaone/identity_272605.jpg
| |
<image>Determine the value of y.
Choices:
(A) \(2 \sqrt{7}\)
(B) 6
(C) 8
(D) 10
|
d
|
geometry3k
|
data/llavaone/identity_316061.jpg
| |
<image>The diameters of three circles are 10, 30, and 10 units, respectively. Find a certain length if it is congruent to another length and that length is 2 units.
Choices:
(A) 2
(B) 4
(C) 10
(D) 30
|
a
|
geometry3k
|
data/llavaone/identity_314212.jpg
| |
<image>What is the value of x in the given similar polygons?
|
13/3
|
geometry3k
|
data/llavaone/identity_89282.jpg
| |
<image>Determine the measure of angle ABD.
Choices:
(A) 97
(B) 103
(C) 126
(D) 154
|
b
|
geometry3k
|
data/llavaone/identity_270376.jpg
| |
<image>Find x.
Choices:
(A) \frac { 17 \sqrt { 2 } } { 2 }
(B) 17
(C) 17 \sqrt { 2 }
(D) 34
|
a
|
geometry3k
|
data/llavaone/identity_30093.jpg
| |
<image>What is the length of line segment AG in polygon A E F G?
|
14
|
geometry3k
|
data/llavaone/identity_85090.jpg
| |
<image>Calculate the perimeter of the figure in feet and round to the nearest tenth, if needed.
Choices:
(A) 8
(B) 14.4
(C) 16
(D) 18.9
|
c
|
geometry3k
|
data/llavaone/identity_262178.jpg
| |
<image>Find m \angle B.
Choices:
(A) 24
(B) 36
(C) 48
(D) 72
|
b
|
geometry3k
|
data/llavaone/identity_1188.jpg
| |
<image>In triangle RST, Z is the centroid and RZ measures 18. Determine the length of ZV.
Choices:
(A) 5
(B) 9
(C) 10
(D) 18
|
b
|
geometry3k
|
data/llavaone/identity_266463.jpg
| |
<image>In rhombus ABCD, if AB = 15 and m∠ABD = 24, what is the length of diagonal BD?
|
18.88
|
geometry3k
|
data/llavaone/identity_159814.jpg
| |
<image>Determine the value of y.
Choices:
(A) 4
(B) 4 \sqrt { 3 }
(C) 8
(D) 8 \sqrt { 3 }
|
b
|
geometry3k
|
data/llavaone/identity_303884.jpg
| |
<image>What is the length of side AD?
|
25.5
|
geometry3k
|
data/llavaone/identity_162644.jpg
| |
<image>Determine the value of x.
Options:
(A) 6
(B) 2√21
(C) 10
(D) 2√29
|
b
|
geometry3k
|
data/llavaone/identity_279276.jpg
| |
<image>Determine the value of y.
Choices:
(A) \(\frac{2}{3} \sqrt{2}\)
(B) \(\frac{2}{3} \sqrt{5}\)
(C) \(2 \sqrt{2}\)
(D) \(2 \sqrt{5}\)
|
b
|
geometry3k
|
data/llavaone/identity_316402.jpg
| |
<image>Find the ratio of the areas of triangle ABC to triangle AED
|
2.04
|
geometry3k
|
data/llavaone/identity_84416.jpg
| |
<image>What is the measure of angle 1?
|
28
|
geometry3k
|
data/llavaone/identity_87037.jpg
| |
<image>What is the value of y if the quadrilateral is a parallelogram?
|
8/5
|
geometry3k
|
data/llavaone/identity_84070.jpg
| |
<image>What is the measure of angle EBD?
|
87
|
geometry3k
|
data/llavaone/identity_81595.jpg
| |
<image>Determine m \widehat T S.
Choices:
(A) 108
(B) 126
(C) 132
(D) 144
|
d
|
geometry3k
|
data/llavaone/identity_315574.jpg
| |
<image>In the figure, \triangle F G H is a right triangle with hypotenuse F H and G J = G H. What is the measure of \angle J G H?
Choices:
(A) 28
(B) 56
(C) 62
(D) 104
|
b
|
geometry3k
|
data/llavaone/identity_11539.jpg
| |
<image>If JKLM is a rectangle and the perimeter is 60 units, what is the length of side KL?
|
15 units
|
geometry3k
|
data/llavaone/identity_163318.jpg
| |
<image>Find the area of the square given that the diagonal is 17
|
144.5
|
geometry3k
|
data/llavaone/identity_252204.jpg
| |
<image>If the rhombus MNPQ is scaled up by a factor of 2, what will be the new area?
|
1500
|
geometry3k
|
data/llavaone/identity_160717.jpg
| |
<image>If m \angle 1 = 3 x + 40, m \angle 2 = 2(y - 10), and m \angle 3 = 2 x + 70, find y.
Choices:
(A) 55
(B) 60
(C) 65
(D) 75
|
d
|
geometry3k
|
data/llavaone/identity_11970.jpg
| |
<image>If L K = 4, M P = 3, P Q = 6, K J = 2, R S = 6, and L P = 2, find the total length of the line segment H M
|
28
|
geometry3k
|
data/llavaone/identity_259238.jpg
| |
<image>In the figure, m \angle 3 = 43. Find the measure of \angle 13.
Choices:
(A) 33
(B) 43
(C) 53
(D) 63
|
b
|
geometry3k
|
data/llavaone/identity_11285.jpg
| |
<image>If m \angle Z Y W = 2 x - 7 and m \angle W Y X = 2 x + 5, find m \angle Z Y W.
Choices:
(A) 13
(B) 23
(C) 39
(D) 46
|
c
|
geometry3k
|
data/llavaone/identity_9721.jpg
| |
<image>If WP is a perpendicular bisector, and m∠WHA = 8q + 17, m∠HWP = 10 + q, find the value of q
|
7
|
geometry3k
|
data/llavaone/identity_163706.jpg
| |
<image>What is the measure of angle AFD?
|
146°
|
geometry3k
|
data/llavaone/identity_90886.jpg
| |
<image>For the trapezoid shown, A and B are midpoints of the legs. If the length of A B is 57 and the length of K L is 21, find the length of J M.
Choices:
(A) 21
(B) 57
(C) 87
(D) 93
|
d
|
geometry3k
|
data/llavaone/identity_333108.jpg
| |
<image>Determine the measure of angle T.
Choices:
(A) 44
(B) 46
(C) 54
(D) 134
|
b
|
geometry3k
|
data/llavaone/identity_305560.jpg
| |
<image>Calculate the area of the figure and round to the nearest tenth, if needed. The options are:
(A) 740
(B) 840
(C) 1050
(D) 1540
|
c
|
geometry3k
|
data/llavaone/identity_280729.jpg
| |
<image>What is the measure of the third angle in the triangle?
|
25
|
geometry3k
|
data/llavaone/identity_159887.jpg
| |
<image>Find the measure of angle FHJ
|
90
|
geometry3k
|
data/llavaone/identity_79574.jpg
| |
<image>Find the measure of \angle 1 if m \angle D G F = 53 and m \angle A G C = 40.
Choices:
(A) 30
(B) 37
(C) 40
(D) 50
|
b
|
geometry3k
|
data/llavaone/identity_11233.jpg
| |
<image>Determine the value of x.
Choices:
(A) \(\frac { 17 \sqrt { 2 } } { 2 }\)
(B) \(\frac { 19 \sqrt { 2 } } { 2 }\)
(C) \(\frac { 21 \sqrt { 2 } } { 2 }\)
(D) \(\frac { 23 \sqrt { 2 } } { 2 }\)
|
b
|
geometry3k
|
data/llavaone/identity_313901.jpg
| |
<image>What is the total length of the pink lines inside the circle?
|
60
|
geometry3k
|
data/llavaone/identity_91606.jpg
| |
<image>In \odot F, A B \cong B C, D F = 3 x - 7, and F E = x + 9. What is x?
Choices:
(A) 4
(B) 7
(C) 8
(D) 9
|
c
|
geometry3k
|
data/llavaone/identity_16109.jpg
| |
<image>Calculate the area of the regular polygon and round to the nearest tenth.
Choices:
(A) 73.0
(B) 292.1
(C) 584.2
(D) 1168.5
|
c
|
geometry3k
|
data/llavaone/identity_280364.jpg
| |
<image>What is the value of y in the parallelogram ABCD?
|
12.67
|
geometry3k
|
data/llavaone/identity_80479.jpg
| |
<image>Find y.
Choices:
(A) 1
(B) 2
(C) 3
(D) 4
|
c
|
geometry3k
|
data/llavaone/identity_13661.jpg
| |
<image>What is the measure of angle CED?
|
50
|
geometry3k
|
data/llavaone/identity_164157.jpg
| |
<image>Find x. Assume that segments that appear to be tangent are tangent.
Choices:
(A) 3
(B) 4
(C) 5
(D) 6
|
a
|
geometry3k
|
data/llavaone/identity_13565.jpg
| |
<image>Find the measure of the exterior angle adjacent to the 32° angle in the triangle containing angle 1
|
117°
|
geometry3k
|
data/llavaone/identity_231435.jpg
| |
<image>Determine the measure of angle 1.
Choices:
(A) \pi
(B) 48
(C) 96
(D) 360
|
b
|
geometry3k
|
data/llavaone/identity_285181.jpg
| |
<image>What is the measure of angle ZWX in the given image?
|
78.5
|
geometry3k
|
data/llavaone/identity_82145.jpg
| |
<image>What is the area of the figure?
|
82
|
geometry3k
|
data/llavaone/identity_88069.jpg
| |
<image>Find x.
Choices:
(A) \frac { \sqrt { 5 } } { 10 }
(B) \frac { \sqrt { 10 } } { 10 }
(C) \frac { \sqrt { 5 } } { 5 }
(D) \frac { \sqrt { 10 } } { 5 }
|
d
|
geometry3k
|
data/llavaone/identity_31650.jpg
| |
<image>Determine the value of x in the diagram.
Choices:
(A) 12
(B) 16
(C) 20
(D) 32
|
b
|
geometry3k
|
data/llavaone/identity_309833.jpg
| |
<image>Determine the value of y.
Choices:
(A) 2
(B) 3
(C) 4
(D) 5
|
d
|
geometry3k
|
data/llavaone/identity_300193.jpg
| |
<image>What is the perimeter of the equilateral triangle RST?
|
81
|
geometry3k
|
data/llavaone/identity_162522.jpg
| |
<image>What is the length of segment AT if AX = 24 and DE = 7?
|
22.18
|
geometry3k
|
data/llavaone/identity_82426.jpg
| |
<image>If JKLM is a rectangle and the length of JM is twice the length of JL, what is the ratio of the area of triangle JPM to the area of the rectangle?
|
1/4
|
geometry3k
|
data/llavaone/identity_163316.jpg
| |
<image>What is the measure of angle JKL?
|
153.5
|
geometry3k
|
data/llavaone/identity_164153.jpg
| |
<image>Find x.
Choices:
(A) 34
(B) 49
(C) 60
(D) 128
|
c
|
geometry3k
|
data/llavaone/identity_7866.jpg
| |
<image>If triangles PQS and RQS are congruent, what is the ratio of side PQ to side QR?
|
2:1
|
geometry3k
|
data/llavaone/identity_165231.jpg
| |
<image>Find y.
Choices:
(A) \frac { 2 } { 3 } \sqrt { 2 }
(B) \frac { 2 } { 3 } \sqrt { 5 }
(C) 2 \sqrt { 2 }
(D) 2 \sqrt { 5 }
|
b
|
geometry3k
|
data/llavaone/identity_16437.jpg
| |
<image>What is the measure of angle QUR in the inscribed equilateral pentagon PQRST?
|
216
|
geometry3k
|
data/llavaone/identity_88891.jpg
| |
<image>Find the length of segment OG if the length of segment LS is 12 units. Round to the nearest tenth, if necessary
|
14.3 units
|
geometry3k
|
data/llavaone/identity_227683.jpg
| |
<image>What is the sum of the interior angles of kite CDFG?
|
360
|
geometry3k
|
data/llavaone/identity_163633.jpg
| |
<image>If c = 8, find the length of side a
|
4
|
geometry3k
|
data/llavaone/identity_162290.jpg
| |
<image>If the trapezoid MNPQ is reflected across line PQ, what will be the area of the resulting figure?
|
720
|
geometry3k
|
data/llavaone/identity_159250.jpg
| |
<image>If this is a kite, find m \angle D.
Choices:
(A) 18
(B) 49
(C) 67
(D) 122
|
d
|
geometry3k
|
data/llavaone/identity_332484.jpg
| |
<image>Determine the value of x.
Choices:
(A) 4
(B) 4√3
(C) 8
(D) 6√3
|
a
|
geometry3k
|
data/llavaone/identity_308400.jpg
| |
<image>What is the circumference of circle Q?
|
8√5π ft
|
geometry3k
|
data/llavaone/identity_82832.jpg
| |
<image>What is the length of side MN in triangle JMN?
|
3
|
geometry3k
|
data/llavaone/identity_81174.jpg
| |
<image>If \( P R \parallel W X \), \( W X = 10 \), \( X Y = 6 \), \( W Y = 8 \), \( R Y = 5 \), and \( P S = 3 \), find the length of \( P Q \)
|
3
|
geometry3k
|
data/llavaone/identity_230376.jpg
| |
<image>Find the value of x and then determine the perimeter of triangle FGH
|
55.89
|
geometry3k
|
data/llavaone/identity_241265.jpg
| |
<image>What is the measure of angle WYU?
|
77.714
|
geometry3k
|
data/llavaone/identity_84600.jpg
| |
<image>In the figure, if m \angle 5 = 120, find the measure of \angle 2
|
120
|
geometry3k
|
data/llavaone/identity_82246.jpg
| |
<image>If the measure of angle p is 120 degrees, what is the measure of angle q in the figure?
|
60
|
geometry3k
|
data/llavaone/identity_82967.jpg
| |
<image>In circle R, if SU = 20 and YW = 20, what is the measure of angle VZW?
|
90
|
geometry3k
|
data/llavaone/identity_87501.jpg
| |
<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.
Choices:
(A) 3
(B) 6
(C) 9
(D) 12
|
b
|
geometry3k
|
data/llavaone/identity_37125.jpg
| |
<image>Find the perimeter of triangle SRT
|
11
|
geometry3k
|
data/llavaone/identity_230809.jpg
| |
<image>Find the measure of the largest angle in the triangle. Round the angle measure to the nearest degree
|
67
|
geometry3k
|
data/llavaone/identity_224976.jpg
| |
<image>Given that XY = 4a - 5 and ST = -5a + 13, find the value of a when XY = ST
|
2
|
geometry3k
|
data/llavaone/identity_84135.jpg
| |
<image>What is the measure of angle TSR?
|
72
|
geometry3k
|
data/llavaone/identity_90425.jpg
| |
<image>What is the perimeter of triangle EDF if the length of segment FT is 12 and the lengths of the other two medians are equal to FT?
|
54
|
geometry3k
|
data/llavaone/identity_84708.jpg
| |
<image>P is the incenter of a triangle. Determine the measure of a certain angle, \( \angle DAC \).
Choices:
(A) 28.5
(B) 30
(C) 31
(D) 33
|
d
|
geometry3k
|
data/llavaone/identity_307436.jpg
| |
<image>Find the perimeter of parallelogram NQRM
|
58
|
geometry3k
|
data/llavaone/identity_260760.jpg
| |
<image>Determine the area of the shaded part. Assume that all polygons that seem regular are regular. Round to the nearest tenth.
Choices:
(A) 25
(B) 28.5
(C) 30.4
(D) 50
|
c
|
geometry3k
|
data/llavaone/identity_308656.jpg
| |
<image>The diameters of \odot A, \odot B, and \odot C are 8 inches, 18 inches, and 11 inches, respectively. Find F G.
Choices:
(A) 7
(B) 8
(C) 14
(D) 16
|
c
|
geometry3k
|
data/llavaone/identity_14461.jpg
| |
<image>Polygon A B C D \sim polygon A E F G, m \angle A G F = 108, G F = 14, A D = 12, D G = 4.5, E F = 8, and A B = 26. Find D C.
Choices:
(A) 12
(B) 14
(C) 22.4
(D) 26
|
c
|
geometry3k
|
data/llavaone/identity_2244.jpg
| |
<image>What is the length of segment QR in the parallelogram QRST?
|
148
|
geometry3k
|
data/llavaone/identity_90461.jpg
| |
<image>What is the length of the hypotenuse of the larger right triangle in the figure above?
|
14√2
|
geometry3k
|
data/llavaone/identity_165282.jpg
| |
<image>What is the area of the circle?
|
16 * pi
|
geometry3k
|
data/llavaone/identity_162060.jpg
| |
<image>Find x.
Choices:
(A) 59
(B) 117
(C) 125
(D) 342
|
a
|
geometry3k
|
data/llavaone/identity_19942.jpg
| |
<image>Find x so that the quadrilateral is a parallelogram.
Choices:
(A) 2
(B) 4
(C) 10
(D) 12
|
a
|
geometry3k
|
data/llavaone/identity_14628.jpg
| |
<image>What is the area of the triangle?
|
40
|
geometry3k
|
data/llavaone/identity_160467.jpg
| |
<image>What is the length of the diagonal of the square?
|
13.57 units
|
geometry3k
|
data/llavaone/identity_81440.jpg
| |
<image>What is the measure of the angle formed by line m and the transversal?
|
140°
|
geometry3k
|
data/llavaone/identity_91525.jpg
| |
<image>What is the measure of angle 5 in the figure?
|
110
|
geometry3k
|
data/llavaone/identity_82964.jpg
| |
<image>Find x. Assume that segments that appear to be tangent are tangent.
Choices:
(A) 2
(B) 2.37
(C) 4
(D) 4.37
|
b
|
geometry3k
|
data/llavaone/identity_37521.jpg
| |
<image>Given that \( m \angle 11 = 4x \) and \( m \angle 12 = 2x - 6 \), determine the measure of \( \angle 12 \).
Choices:
(A) 50
(B) 52
(C) 56
(D) 62
|
c
|
geometry3k
|
data/llavaone/identity_308234.jpg
| |
<image>What is the measure of each interior angle of the regular polygon?
|
60
|
geometry3k
|
data/llavaone/identity_85897.jpg
| |
<image>Determine the value of h.
Options:
(A) 3
(B) 6
(C) 6 √2
(D) 6 √3
|
b
|
geometry3k
|
data/llavaone/identity_295980.jpg
|
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