data_source stringclasses 1
value | images images listlengths 1 1 | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|---|
multimodal_opensource_math | [
{
"content": "<image>Consider a right-angled triangular plate with a 30° angle, where both ends of the plate are positioned on opposite sides of a ruler. If angle 1 = 22°, express the measure of angle 2\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "38°",
"style": "rule"
} | {
"difficulty": "1",
"index": "5ac1b470-2033-4df7-bd05-3c0cfe0196bb"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the degree measure of angle OAB in the scenario where BC is the diameter of circle O and AB is a chord of circle O, with angle AOC measuring 60 degrees?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "30°",
"style": "rule"
} | {
"difficulty": "1",
"index": "92111c4a-718d-4116-81ff-51877736ef9c"
} | |
multimodal_opensource_math | [
{
"content": "<image>Figure 1 shows a tall cup filled with liquid (data as shown in the figure). After some of the liquid is removed, it is placed on a horizontal tabletop as shown in Figure 2. At this time, the liquid level AB = ()\nLet's think step by step and output the final answer within \\boxed{}.",
"... | MATH | {
"ground_truth": "3cm",
"style": "rule"
} | {
"difficulty": "1",
"index": "91568c58-f583-42af-ad04-90f8eab38f2c"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the ABCD shape is a combination of a rectangle and a semi-circle, the perimeter of the ABCD shape is 92, the BCFG shape is a combination of a rectangle and a semi-circle, the perimeter of the BCFG shape is 84 and the arc length of the ICF sector is 23.13, compute the length of the AB sid... | MATH | {
"ground_truth": "20.95",
"style": "rule"
} | {
"difficulty": "1",
"index": "e115c5fe-6e81-4a81-8825-0d2772f2a03c"
} | |
multimodal_opensource_math | [
{
"content": "<image>The aerial drone measured the elevation angle of the top B of a building from A to be 120 degrees, and the depression angle of the bottom C is 240 degrees. At this time, the horizontal distance AD between the aerial drone and the building is 360 units, then the height of the building BC i... | MATH | {
"ground_truth": "480√{3}",
"style": "rule"
} | {
"difficulty": "1",
"index": "a3175f0b-5538-4573-8609-d8d302ce4890"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the trapezoidal rock dam's slope AB has a ratio of 1.0:3.0 and slope BC measures 2.0, what is the length of slope AB in the figure?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "2√{10}m",
"style": "rule"
} | {
"difficulty": "1",
"index": "f0a384f0-2020-45a1-b053-96464c710cf3"
} | |
multimodal_opensource_math | [
{
"content": "<image>Let ABCD be a parallelogram with point E as the midpoint of side BC and point F as the midpoint of side AD. If the length of AE is given by 'a' and the length of DE is denoted by 'b', what is the formula for the length of AB in terms of 'a' and 'b'?\nLet's think step by step and output the ... | MATH | {
"ground_truth": "5",
"style": "rule"
} | {
"difficulty": "1",
"index": "3ad56b5f-0b50-43b4-9fa0-1475a55ef0b1"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle W. Points D, S, U, X, Y lie on the circle W. Which lines are equal in length to line WD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "WS, WU, WX, WY",
"style": "rule"
} | {
"difficulty": "1",
"index": "7439ad8a-9a9d-4f48-9841-592d1dce5ab0"
} | |
multimodal_opensource_math | [
{
"content": "<image>Compute the length of the BC side of the ABC right triangle. Round computations to 2 decimal places.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "16.73",
"style": "rule"
} | {
"difficulty": "1",
"index": "b7073b20-6b95-44a9-9a41-4ea833b67aa6"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, rotate triangle ABC counterclockwise around point A by a certain angle to obtain triangle ADE. Given angle B = x, angle CAE = y, and angle DAC = z, determine the value of z\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
... | MATH | {
"ground_truth": "20°",
"style": "rule"
} | {
"difficulty": "1",
"index": "90a002c8-fd8f-412b-9a02-6f7fca73ba2c"
} | |
multimodal_opensource_math | [
{
"content": "<image>Find D B.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "5",
"style": "rule"
} | {
"difficulty": "1",
"index": "93335f9a-6978-48b9-a251-bde81bd378bd"
} | |
multimodal_opensource_math | [
{
"content": "<image>Line TI is the line connecting the midpoint T of line BF and the midpoint I of line QC. What is the length of line TB if the length of line BF is 6?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "3",
"style": "rule"
} | {
"difficulty": "1",
"index": "44bc194b-ebd0-46c6-b5e6-7b7f8a4a1848"
} | |
multimodal_opensource_math | [
{
"content": "<image>As depicted in the figure, with angle A measuring 28.0 degrees, angle BFC measuring 92.0 degrees, and angle B being congruent to angle C, what is the degree measure of angle BDC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "60°",
"style": "rule"
} | {
"difficulty": "1",
"index": "ba5c2b8a-4910-4aaf-b417-351af2113a09"
} | |
multimodal_opensource_math | [
{
"content": "<image>Let A be a point on circle O, and let's denote the central angle OCB as variable h where h = 40.0 degrees. What is the degree measure of angle A, expressed as variable k in relation to h?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "50°",
"style": "rule"
} | {
"difficulty": "1",
"index": "0f7520c2-8856-4068-ab5f-a4d5fc7f6fb6"
} | |
multimodal_opensource_math | [
{
"content": "<image>Determine the measure of angle 1.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "59",
"style": "rule"
} | {
"difficulty": "1",
"index": "8f53dd34-67ed-46e4-b2b3-47867958d7b7"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the provided figure, triangle ABC is depicted with a right angle at C. Three squares are constructed outside triangle ABC, with their sides coinciding with the sides of the triangle. Denoting the areas of these squares as S1, S2, and S3 respectively, if S1 equals 2 and S3 equals 5, what ... | MATH | {
"ground_truth": "7",
"style": "rule"
} | {
"difficulty": "1",
"index": "436b00e9-76ea-48c2-86a3-8818218bc7ec"
} | |
multimodal_opensource_math | [
{
"content": "<image>In triangle ABC, point M is the midpoint of side BC, point N is the angle bisector of the exterior angle at A, and point N is perpendicular to line AN at point N. Given that AB = 4.0 and MN = 2.8, what is the length of AC? Express the length of AC as 'x'\nLet's think step by step and output... | MATH | {
"ground_truth": "1.6",
"style": "rule"
} | {
"difficulty": "1",
"index": "b59d29fe-8fec-4419-975c-96f7631ed17f"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given triangle ABC, if the folding of triangle ABC along line DE causes point C to fall outside the quadrilateral ABDE, and it is determined that angle 1 = 108° and angle C = 35°, what is the measure of angle 2? Express the measure of angle 2 as 'x' degrees\nLet's think step by step ... | MATH | {
"ground_truth": "38°",
"style": "rule"
} | {
"difficulty": "1",
"index": "f540cc0d-956e-4cd2-b262-482465eaa37e"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the provided diagram, let's represent the length of AC as variable u where u = 10.0 and the measure of angle P as variable v where v = 30.0. What is the length of AB, expressed as variable w in relation to u and v?\nLet's think step by step and output the final answer within \\boxed{}.",... | MATH | {
"ground_truth": "5√{3}",
"style": "rule"
} | {
"difficulty": "1",
"index": "8ec1f0d5-41e7-4351-9c60-df52f6f1ec7c"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the parallelogram ABCD is depicted with AB measuring 10 units and BC measuring 6 units, and E, F being the midpoints of AD and DC respectively, and EF measuring 7 units, then what is the perimeter of quadrilateral EACF?\nLet's think step by step and output the final answer within \\boxed... | MATH | {
"ground_truth": "29",
"style": "rule"
} | {
"difficulty": "1",
"index": "b50a9bdd-386c-4089-b7df-0de38b759c4f"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, the measure of angle GIB is 119 degrees, and the line KR is perpendicular to the line NY at point G. What is the measure of angle GKB?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "71 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "13606710-4ff5-4d2e-8587-207754c8c264"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given that AE=10 and BE=24 in the diagram, what is the length of diagonal AC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "26",
"style": "rule"
} | {
"difficulty": "1",
"index": "515606c5-8a5d-412b-89eb-010ed43af4f0"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle A. There are lines AG, OK, VU in the diagram. Which lines are equal in length to line AG?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "AO, AK, AV, AU",
"style": "rule"
} | {
"difficulty": "1",
"index": "c6601946-7ecb-4ea3-985a-6fad26ab14a1"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle G with a diameter of 4.6. What is the circumference of the circle G? Approximating π≈3.14.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "14.45",
"style": "rule"
} | {
"difficulty": "1",
"index": "d4eae453-422f-4395-9679-f961a8bbd28e"
} | |
multimodal_opensource_math | [
{
"content": "<image>Within the figure displaying triangle ABC, points D and E are indicated on sides AB and AC respectively, with DE being parallel to BC. When it is given that AD measures 2.0 units, DB measures 1.0 unit, and DE measures 1.6 units, what can be determined about the length of BC?\nLet's think st... | MATH | {
"ground_truth": "2.4cm",
"style": "rule"
} | {
"difficulty": "1",
"index": "7c2153a6-4060-4855-8869-02b8738a539c"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is an equilateral triangle in the diagram, represented by the symbol AWZ. The length of line WZ is 7. Line HG is the line connecting the midpoint H of line ZA and the midpoint G of line AW. What is the length of line AG?\nLet's think step by step and output the final answer within \\b... | MATH | {
"ground_truth": "3.5",
"style": "rule"
} | {
"difficulty": "1",
"index": "32b5e30e-fa68-4251-9cd4-78e78d58a489"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle V. The measure of the angle FVM is equal to 67 degrees. The measure of the angle MVU is equal to 88 degrees. The measure of the angle UVP is equal to 44 degrees. The measure of the angle PVG is equal to 87 degrees. What is the measure of angle VGF?\nLet's t... | MATH | {
"ground_truth": "74 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "220b6636-2862-4554-88d0-e9545f1af235"
} | |
multimodal_opensource_math | [
{
"content": "<image>ND is the extension line of TN. What does this mean in terms of collinearity?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "T, N, and D are collinear",
"style": "rule"
} | {
"difficulty": "1",
"index": "801b4a3d-4cd8-4644-97ab-df41ff1796f9"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is an equilateral triangle in the diagram, represented by the symbol ICT. Line GU is the line connecting the midpoint G of line IC and the midpoint U of line CT. What is the length of line GC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"... | MATH | {
"ground_truth": "6",
"style": "rule"
} | {
"difficulty": "1",
"index": "0cddcb49-d920-423a-ac59-67d24b3e0461"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a trapezoid in the diagram, represented by the symbol MCFY. Line HE is the line connecting the midpoint H of line YM and the midpoint E of line CF. What is the length of line HM if the length of line YM is 8?\nLet's think step by step and output the final answer within \\boxed{}.",... | MATH | {
"ground_truth": "4",
"style": "rule"
} | {
"difficulty": "1",
"index": "315a0b7d-05c7-48fe-9e84-a7cdfb87e086"
} | |
multimodal_opensource_math | [
{
"content": "<image>ED is the line connecting the midpoint E of line WY and the midpoint D of line JL. What is the length of EW if the length of WY is 16?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "8",
"style": "rule"
} | {
"difficulty": "1",
"index": "202c2491-8d9c-403b-9edb-ac7d77c64e1a"
} | |
multimodal_opensource_math | [
{
"content": "<image>Let ABCD be a quadrilateral with diagonals AC and BD intersecting at point O. Given that AE = EB, OE = 3, and AB = 5, express the perimeter of ABCD in terms of its side lengths and the length of OE\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
... | MATH | {
"ground_truth": "22",
"style": "rule"
} | {
"difficulty": "1",
"index": "c8610eda-44f6-451b-a61e-19dc43013367"
} | |
multimodal_opensource_math | [
{
"content": "<image>In triangle ABC, where AB is equal to AC and angle A measures 50.0 degrees, if the vertical bisector of AB intersects AC at point D and the perpendicular foot is labeled as E, what is the degree measure of angle DBC?\nLet's think step by step and output the final answer within \\boxed{}.",
... | MATH | {
"ground_truth": "15°",
"style": "rule"
} | {
"difficulty": "1",
"index": "73c7a913-c9d9-4e65-93e4-b89245c4e30d"
} | |
multimodal_opensource_math | [
{
"content": "<image>If in the provided figure, line a is parallel to line b, angles 1 and 2 are complementary, and angle 3 is equal to 115.0 degrees, what is the degree measure of angle 4?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "155°",
"style": "rule"
} | {
"difficulty": "1",
"index": "c240a654-290b-4917-a6d7-f0dd245237d0"
} | |
multimodal_opensource_math | [
{
"content": "<image>If DE is the perpendicular bisector of AB in right triangle ABC, and intersects AC at E, what is the ratio of AE to EC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "1:1",
"style": "rule"
} | {
"difficulty": "1",
"index": "4d20b856-9f2c-4468-b56c-39b0d6d26338"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given in the figure is triangle ABC, where AB is equal to AC. Two arcs are drawn using points A and B as centers, and they intersect at points E and F. The line EF is then drawn. The midpoint of BC is labeled as point D, and any point on line EF is denoted as M. If the length of BC is 5 and... | MATH | {
"ground_truth": "6",
"style": "rule"
} | {
"difficulty": "1",
"index": "ebc40d4c-404a-4ad9-9d62-fd47da05b167"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given diagram, there is a circle O with a tangent AD at point A. The line DO intersects circle O at point C, and point B lies on the circle. When connecting lines AB and CB, what is the degree measure of angle ABC if angle D measures 36 degrees?\nLet's think step by step and output t... | MATH | {
"ground_truth": "27°",
"style": "rule"
} | {
"difficulty": "1",
"index": "c8497080-ed50-48c2-a284-84a7a5275d8c"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the equilateral triangle ABC shown in the image, with AD perpendicular to BC and E as a point on AD, if ∠CED is 50°, what is the measure of ∠CDE?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "40°",
"style": "rule"
} | {
"difficulty": "1",
"index": "7cf6847e-d8df-4b9f-a02d-ca530acf8004"
} | |
multimodal_opensource_math | [
{
"content": "<image>The line FU is the tangent line of the circle W at point K. What is the measure of angle WKF?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "90 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "0f01b2ec-4a5f-466b-aaea-e08ba426af72"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, if line AB is parallel to line CD, and the ratio of angle 1 to angle 2 is 7:11, then what is the measure of angle 2 in degrees?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "110°",
"style": "rule"
} | {
"difficulty": "1",
"index": "504fb77d-80ca-4635-9fc7-04974deee55c"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle Z with diameter TE. What is the measure of angle TZE?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "90 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "ad859257-ddac-4915-9545-b080ac769257"
} | |
multimodal_opensource_math | [
{
"content": "<image>If we examine the figure given, which illustrates AB as the diameter of a semicircle centered at O, and includes C and D as points on the semicircle, what is the measure of angle D when angle ACO has a measurement of 20 degrees?\nLet's think step by step and output the final answer within \... | MATH | {
"ground_truth": "110°",
"style": "rule"
} | {
"difficulty": "1",
"index": "bcc279e4-d9a3-4fd2-a42e-36e886250877"
} | |
multimodal_opensource_math | [
{
"content": "<image>In circle O, where AB is the diameter, C is a point on the extended line of AB, and CD is the tangent of circle O at point D, if angle A measures 'p' degrees, AB measures 'q' units, and OA is equal to OD, what is the length of CD? Express the length of CD as a function of 'p' and 'q'\nLet's... | MATH | {
"ground_truth": "√{3}cm",
"style": "rule"
} | {
"difficulty": "1",
"index": "2cac06c3-41b1-41b9-8d31-0b9bc42eb3a8"
} | |
multimodal_opensource_math | [
{
"content": "<image>Consider the diamond ABCD with diagonal AC of length 'd1' units and diagonal BD of length 'd2' units. If point E coincides with point A on the extended line of CB, what will be the area 'A' of quadrilateral AEBD expressed in terms of 'd1' and 'd2'?\nLet's think step by step and output the f... | MATH | {
"ground_truth": "24",
"style": "rule"
} | {
"difficulty": "1",
"index": "a5acdb46-8c57-495c-b485-4d3f774345d5"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, parallelogram ABCD has side lengths AB and BC equal to 6.0 and 10.0 units respectively. Point E is situated before point AD, with the given property that BE is equal to BC, and CE is equal to CD. How long is the segment DE?\nLet's think step by step and output the fi... | MATH | {
"ground_truth": "3.6",
"style": "rule"
} | {
"difficulty": "1",
"index": "53fea198-3ace-4680-8d94-cbc3bccba303"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the figure, in quadrilateral ABCD, the angle bisector AG of angle BAD intersects BC at point E. If BF = 12 and AB = 10, what is the length of AE?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "16",
"style": "rule"
} | {
"difficulty": "1",
"index": "7a3e6114-7035-4aba-a522-aba419bb2560"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram showing square ABCD and point E on diagonal BD, if angle BCE is measured at 70°, what is the measure of angle EAD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "20°",
"style": "rule"
} | {
"difficulty": "1",
"index": "2f060fd9-f22f-4558-a4e8-127709299ffb"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a triangle RXE. The measure of angle XRE is equal to 67 degrees. What is the measure of angle XRE?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "67 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "46b2c48a-5502-488a-92d8-e38c44dcdbb9"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a square in the diagram, represented by the symbol UGZS. The length of line SU is 13. What is the length of line GZ?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "13",
"style": "rule"
} | {
"difficulty": "1",
"index": "d85396eb-8780-4c9b-a773-bc125fe205fb"
} | |
multimodal_opensource_math | [
{
"content": "<image>As depicted in the figure, if the longest chord cutting point M in circle O measures 10.0 cm and the shortest chord crossing point M measures 8.0 cm, what is the length of OM?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "3厘米",
"style": "rule"
} | {
"difficulty": "1",
"index": "150536e9-6bb2-4fec-9c9b-7582473a3d36"
} | |
multimodal_opensource_math | [
{
"content": "<image>If in ∆PQR, points X, Y, and Z are midpoints of sides QR, PR, and PQ respectively, and the area of ∆PQR is denoted as 'T', then what is the area of ∆XYZ in relation to 'T'?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "0.5cm2",
"style": "rule"
} | {
"difficulty": "1",
"index": "377e7e85-4c37-4a00-b283-902a422361b8"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the provided diagram, let's assign the measure of angle ABC as variable h, where h = 52.0 degrees. What is the degree measure of angle AOC, represented as variable w in relation to h?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "104°",
"style": "rule"
} | {
"difficulty": "1",
"index": "4e03bb0b-08e0-43f4-bc29-dbe3c94cb6b7"
} | |
multimodal_opensource_math | [
{
"content": "<image>Compute the arc length of the red sector. Assume $\\pi=3.14$. Round computations to 2 decimal places.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "7.91",
"style": "rule"
} | {
"difficulty": "1",
"index": "f1f1f889-9e4c-4fe4-b245-1083a2deb841"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, triangular plates are arranged as shown. If the degree measure of angle 2 is 20 more than angle 1, what is the degree measure of angle 1?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "35°",
"style": "rule"
} | {
"difficulty": "1",
"index": "d3e0c7d7-047b-4321-8e9a-d587ac38e343"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the figure provided, if a triangle has its right angle vertex positioned on one side of a ruler and angle 1 is 50°, what is the measurement of angle 2?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "40°",
"style": "rule"
} | {
"difficulty": "1",
"index": "a65c7815-392c-461c-8057-70b724581380"
} | |
multimodal_opensource_math | [
{
"content": "<image>When considering the provided figure, if angle 1 is determined to be 50 degrees, what is the measurement of angle 2?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "130°",
"style": "rule"
} | {
"difficulty": "1",
"index": "5cb393e3-d1c6-4e46-be8a-099639f7c94c"
} | |
multimodal_opensource_math | [
{
"content": "<image>Triangle ABC is depicted in the diagram, with point D located on side BC, and it is stated that angle BAD is congruent to angle C. Find the length of AB given that BD is 2 and CD is 4\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "2√{3}",
"style": "rule"
} | {
"difficulty": "1",
"index": "76cb226a-e005-4bf0-a410-de8027048369"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the limit of the function as x approaches 1 from the right side?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "-8",
"style": "rule"
} | {
"difficulty": "1",
"index": "a0abb32f-97d1-4b72-abfe-8e0053014027"
} | |
multimodal_opensource_math | [
{
"content": "<image>Circle O is depicted in the diagram, with tangents PA and PB at points A and B respectively. Point C is located on the circle. If angle ACB is measured at 62°, what is the degree measure of angle P?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"... | MATH | {
"ground_truth": "56°",
"style": "rule"
} | {
"difficulty": "1",
"index": "d82b90a1-8715-4dcd-956d-7036ec201dc7"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, AB, BC, and CD are all tangent to the semicircle. Where AB = 4.0, CD = 9.0, BC = 13.0, the radius of the semicircle is ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "6",
"style": "rule"
} | {
"difficulty": "1",
"index": "59ec74cc-7381-4803-ae21-55467a312a53"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle V. The length of the line TU is equal to 0.31. The length of the line UO is equal to 0.57. What is the length of the line TO?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "0.88",
"style": "rule"
} | {
"difficulty": "1",
"index": "c7174394-43f6-4a6b-be5b-13c0a060f3e1"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a triangle CUV. The measure of angle UCV is equal to 45 degrees. What is the sum of the measures of angles CUV and CVU?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "135 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "9271a717-d922-4e1e-b0b9-0ce0b4058435"
} | |
multimodal_opensource_math | [
{
"content": "<image>In triangle ABC, given that AB = AC, BC = 45.0, point D is on the side AB, and BD = 25.0, translate the line segment BD along the direction of BC to obtain the line segment EF. If the translation distance is 30.0, and the point F is exactly falling on AC, what is the perimeter of triangle C... | MATH | {
"ground_truth": "65.0",
"style": "rule"
} | {
"difficulty": "1",
"index": "b6a7ae5c-9394-4a0a-bf0b-246537a4a154"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given triangle UVW, where UW is perpendicular to VW, UX is the angle bisector of angle UVW, and XY is perpendicular to UV at point Y, if UV = s and VW = t, what is the value of VY expressed using 's' and 't'?\nLet's think step by step and output the final answer within \\boxed{}.",
"rol... | MATH | {
"ground_truth": "4cm",
"style": "rule"
} | {
"difficulty": "1",
"index": "d468a23b-7235-419b-b227-b47688e3e277"
} | |
multimodal_opensource_math | [
{
"content": "<image>If in triangle ABC, points D and E are located on sides AB and AC, satisfying DE to be parallel to BC, and given that AD equals 3.0, BD equals 2.0, and AE equals 2.0, what is the length of EC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "\\frac{4}{3}",
"style": "rule"
} | {
"difficulty": "1",
"index": "eb5930c2-ad4e-4a16-b0e8-d3d4a9efa84d"
} | |
multimodal_opensource_math | [
{
"content": "<image>In a triangle PQR, if the sides PQ = PR = x and side QR = y, calculate the sine of angle Q. Utilize the respective values of 'x' and 'y' in your solution\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "\\frac{12}{13}",
"style": "rule"
} | {
"difficulty": "1",
"index": "a247b9bc-dc27-4900-8b9a-a22ec42cb0e7"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the figure, let BC be the diameter of circle O. If the degree of the arc AC measures 50.0, what is the degree measure of angle ACB? Represent the measure of angle ACB as 'θ'\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "65°",
"style": "rule"
} | {
"difficulty": "1",
"index": "ad9d71d5-f4df-40d4-bd9a-01497bf727ab"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a parallelogram in the diagram, represented by the symbol QZAD. Which sides are parallel to line QZ?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "line AD",
"style": "rule"
} | {
"difficulty": "1",
"index": "a4101ea1-f2f0-4893-8db6-05dbb8ddcc25"
} | |
multimodal_opensource_math | [
{
"content": "<image>How many objects are cylinders?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "2",
"style": "rule"
} | {
"difficulty": "1",
"index": "cb071924-3081-4263-a3b5-113a5404e53d"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle N. The line SI is the chord of the circle N with a length of 1.68. The length of the line MF is equal to 0.75. Can we directly use these chord lengths to calculate the radius of the circle?\nLet's think step by step and output the final answer within \\boxe... | MATH | {
"ground_truth": "no",
"style": "rule"
} | {
"difficulty": "1",
"index": "c5ad96a3-16de-4d16-a70d-a22bb04cf46a"
} | |
multimodal_opensource_math | [
{
"content": "<image>The line ZY is the tangent line of the circle A at point B. What is the measure of angle YBZ?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "90 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "a90562c2-5273-4e0c-824c-0278de46510a"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle T. Point L, Point J, Point G and Point N lie on the circle T. Which lines are equal in length to line TL?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "TJ, TG, TN",
"style": "rule"
} | {
"difficulty": "1",
"index": "f69d1226-f653-4f9d-9d7d-e30df246b878"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given that angle C equals 34.0 degrees and points A, B, and C are on circle O in the figure, what would be the measure of angle AOB?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "68°",
"style": "rule"
} | {
"difficulty": "1",
"index": "131f3b94-5fab-4be4-8c02-af282365a3b0"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a rhombus in the diagram, represented by the symbol CAZS. The length of line CA is 4. What is the length of line AZ?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "4",
"style": "rule"
} | {
"difficulty": "1",
"index": "56f3d820-5a0d-4b65-91ff-5e82c9a9c725"
} | |
multimodal_opensource_math | [
{
"content": "<image>How many objects are made of rubber?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "0",
"style": "rule"
} | {
"difficulty": "1",
"index": "ea09eafc-da0f-4242-bc79-1d282ec38dbd"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given that angle A + angle C equals 120 degrees in parallelogram ABCD, what is the measurement of angle D, as per the diagram representation?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "120°",
"style": "rule"
} | {
"difficulty": "1",
"index": "96075dfd-cb46-4517-a2c7-e25cc08a37b7"
} | |
multimodal_opensource_math | [
{
"content": "<image>How many nodes are in this empty graph?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "32",
"style": "rule"
} | {
"difficulty": "1",
"index": "1e799dfb-60f1-44d9-b07e-e659484d66f4"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle I. There are lines TS, TW, IN, IP in the diagram. Point T, Point S, and Point W lie on the circle I. Which lines are equal in length to line IT?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "IS, IW",
"style": "rule"
} | {
"difficulty": "1",
"index": "c9f1ed28-55a4-47d8-8abc-6706cd19b5e2"
} | |
multimodal_opensource_math | [
{
"content": "<image>Line WZ is perpendicular to line QV. What is the measure of angle WZQ?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "90 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "c889f2cc-0238-4b00-a502-9379b10e94bf"
} | |
multimodal_opensource_math | [
{
"content": "<image>Determine y.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "20",
"style": "rule"
} | {
"difficulty": "1",
"index": "37aac7aa-1f2f-41f6-bfcd-a31607f4a717"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, in triangle ABC, angle C = 90.0, angle BAC = 70.0, rotate triangle ABC clockwise around point A by 70.0, B and C after the corresponding points are B′ and C′ respectively, connect BB′, then angle The degree of B′BC′ is ()\nLet's think step by step and output the fina... | MATH | {
"ground_truth": "55°",
"style": "rule"
} | {
"difficulty": "1",
"index": "eafa08c4-8e55-4773-b59a-6976178e2de6"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram provided, where parallelogram ABCD is shown and its diagonals intersect at point E, if side AB is measured at 5cm and the perimeter of triangle ABE is 3cm less than the perimeter of triangle BEC, what is the length of side AD?\nLet's think step by step and output the final an... | MATH | {
"ground_truth": "8cm",
"style": "rule"
} | {
"difficulty": "1",
"index": "0b284723-6f44-4313-8fe9-5c0ae45cb357"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the perimeter of the entire figure?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "101.24",
"style": "rule"
} | {
"difficulty": "1",
"index": "23064f0e-21d2-4ff8-884c-1678c85318a0"
} | |
multimodal_opensource_math | [
{
"content": "<image>Line OZ is the line connecting point O and the midpoint Z of line KG. What is the length of line OZ if the length of line KG is 10?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "5",
"style": "rule"
} | {
"difficulty": "1",
"index": "8fc9c677-09be-437e-9042-cc929e27b918"
} | |
multimodal_opensource_math | [
{
"content": "<image>In triangle ABC as illustrated, points D and E are positioned on edges AB and AC respectively, with DE being parallel to BC. If AD measures 5.0 units, BD measures 10.0 units, and AE measures 3.0 units, what is the magnitude of CE?\nLet's think step by step and output the final answer within... | MATH | {
"ground_truth": "6",
"style": "rule"
} | {
"difficulty": "1",
"index": "ee09bb7f-2d7f-48e0-b131-3b9c35bede11"
} | |
multimodal_opensource_math | [
{
"content": "<image>If ∠MAB = 30° and BC is the diameter of the circle with center O, what is the measure of ∠ACB?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "90°",
"style": "rule"
} | {
"difficulty": "1",
"index": "5fb18022-0a0f-4b37-8ac9-d63dd449c035"
} | |
multimodal_opensource_math | [
{
"content": "<image>In triangle ABC, let's represent the midpoints of BC, AD, and BE as points D, E, and F respectively. Given that the area of triangle BED is 3cm^2, what is the expression for the area of triangle ABC in terms of the area of triangle BED?\nLet's think step by step and output the final answer ... | MATH | {
"ground_truth": "12",
"style": "rule"
} | {
"difficulty": "1",
"index": "efdbdfff-cf09-407a-ba73-53198d56bc9c"
} | |
multimodal_opensource_math | [
{
"content": "<image>When Xiaoming moves from point A towards point B in a direction 40.0 degrees east of north, and subsequently from point B towards point C in a direction 20.0 degrees east of south, what is the degree measure of angle ABC according to the figure?\nLet's think step by step and output the fina... | MATH | {
"ground_truth": "110°",
"style": "rule"
} | {
"difficulty": "1",
"index": "2fb44f61-21f9-4a3c-957e-d3445df57b1f"
} | |
multimodal_opensource_math | [
{
"content": "<image>Line RO is the line connecting the midpoint R of line QH and the midpoint O of line HJ. What is the length of line RQ if the length of line QH is 8?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "4",
"style": "rule"
} | {
"difficulty": "1",
"index": "837ddcd9-be88-48ca-864d-59c2c13f44e9"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, the line UJ is the diameter of the circle Y, and its length is 3.3. What is the radius of the circle Y?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "1.65",
"style": "rule"
} | {
"difficulty": "1",
"index": "8c1577a9-339a-4e47-afcc-aa08fe051237"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the ABCD shape is a rectangle where a semi-circle has been removed from one side of it and the perimeter of the ABCD shape is 60, compute the length of the AB side of the ABCD shape. Assume $\\pi=3.14$. Round computations to 2 decimal places.\nLet's think step by step and output the fina... | MATH | {
"ground_truth": "21",
"style": "rule"
} | {
"difficulty": "1",
"index": "56141b57-5a3c-4b16-a4ed-5b3551606c06"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle M with a radius of 1.4. What is the area of the circle M?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "6.157521601",
"style": "rule"
} | {
"difficulty": "1",
"index": "bb865cf0-a924-450a-b197-7dbed4d29696"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, in right triangle ABC, given that angle BAC is 90 degrees and angle ABC is 30 degrees, Q is a point on AB, and circle O is tangent to AC and BC at points A and D, and intersects AB at another point E. If BE is 10 units, what is the length of the tangent CD?\nLet's think... | MATH | {
"ground_truth": "10√{3}",
"style": "rule"
} | {
"difficulty": "1",
"index": "7c0da262-bb40-417c-b258-f9a221f172bf"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the diagonal of the gray square is 24, compute the perimeter of the gray square. Round computations to 2 decimal places.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "68.08",
"style": "rule"
} | {
"difficulty": "1",
"index": "b64453bd-8d66-400f-8683-8dc96d54573c"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given diagram, the length of an escalator in a shopping mall is 10 meters, and the height it reaches is 6 meters. The angle formed between the escalator and the ground is denoted by θ. What is the value of tanθ?\nLet's think step by step and output the final answer within \\boxed{}."... | MATH | {
"ground_truth": "3/4",
"style": "rule"
} | {
"difficulty": "1",
"index": "743db4ac-39e5-4933-9711-8a6b2bc9a7df"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given quadrilateral ABCD, AB is parallel to CD, AB = AC = AD = 16.0, BC = 8.0, then what is the length of BD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "8√{15}",
"style": "rule"
} | {
"difficulty": "1",
"index": "7649edd6-578f-4cc1-9de5-c70f066fa467"
} | |
multimodal_opensource_math | [
{
"content": "<image>Subtract all blue objects. How many objects are left?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "2",
"style": "rule"
} | {
"difficulty": "1",
"index": "6521ab42-596b-4b82-862a-7f0946435b9f"
} | |
multimodal_opensource_math | [
{
"content": "<image>In rectangle ABCD, with diagonals AC and BD intersecting at point O, a perpendicular line OE is drawn from O to BD, meeting AD at point E. If AB measures 2 units and the area of triangle DOE is 1.25 square units, what is the length of segment AE denoted as 'x'?\nLet's think step by step and... | MATH | {
"ground_truth": "1.5",
"style": "rule"
} | {
"difficulty": "1",
"index": "81e51d02-6251-4b81-85d0-4668942aaf46"
} | |
multimodal_opensource_math | [
{
"content": "<image>Let A, B, and C be three points on the circle O. If angle B measures 32°, what is the measure of angle OAC? Express the measure of angle OAC as θ\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "58°",
"style": "rule"
} | {
"difficulty": "1",
"index": "cc698e29-bdc3-4d95-8e0b-8860424ddcb5"
} | |
multimodal_opensource_math | [
{
"content": "<image>In Figure 1, if angle B is represented by the variable 'x' (x = 70.0) and angle C is represented by the variable 'y' (y = 80.0), what is the measure of angle MNB? Express the angle as 'z' in terms of 'x' and 'y'\nLet's think step by step and output the final answer within \\boxed{}.",
"... | MATH | {
"ground_truth": "95",
"style": "rule"
} | {
"difficulty": "1",
"index": "0fa5311c-b37d-4161-a972-4d3bd7fe9182"
} |
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