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>Line IX is the line connecting point I and the midpoint X of line DS. What is the length of line XD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "7.5",
"style": "rule"
} | {
"difficulty": "1",
"index": "51969539-da88-481b-a1b8-0dc8d7f1cbb8"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given the circumcircle O of triangle ABC, where AB = AC and angle A has a measurement of α°, determine the angle measure of BDC in terms of α\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "75°",
"style": "rule"
} | {
"difficulty": "1",
"index": "6a71ed79-72ab-4194-9801-a2aea38abea5"
} | |
multimodal_opensource_math | [
{
"content": "<image>Let's denote the measure of angle AOC as variable 'u' where u = 50.0 degrees. In the given diagram, AB is the diameter of circle O, and C and D are two points on the circle. What is the degree measure of angle D, expressed as variable 'v' in relation to 'u'?\nLet's think step by step and ou... | MATH | {
"ground_truth": "25°",
"style": "rule"
} | {
"difficulty": "1",
"index": "28be6522-e9e6-4a66-a932-bb215589fe39"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the ABCD shape is a combination of a rectangle and a semi-circle, the area of the ABCD shape is 108, the perimeter of the BFGC rectangle is 60, the BFHIJ shape is a combination of a rectangle and an equilateral triangle and the perimeter of the BFHIJ shape is 108, compute the length of t... | MATH | {
"ground_truth": "11.46",
"style": "rule"
} | {
"difficulty": "1",
"index": "1024e2aa-5ad8-4fec-a139-ea27fc27cb77"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a rhombus in the diagram, represented by the symbol DVMW. 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": "DM, MV, VW",
"style": "rule"
} | {
"difficulty": "1",
"index": "06ecabc0-927a-44c5-9c71-4cb4b83ec084"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, it is the situation where two wooden boards A and B are placed on the ground. In the figure, angle 1 and angle 2 are the angles between the two boards A and B and the ground respectively, and angle 3 is the angle between the two boards. If angle 3 = 110.0, then angle... | MATH | {
"ground_truth": "70°",
"style": "rule"
} | {
"difficulty": "1",
"index": "81dc1fe4-0843-4ca4-9a80-0e523eab2081"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given diagram, let's represent the length of AM as variable u (u = 2.0), the length of DE as variable v (v = 1.0), and the length of EF as variable w (w = 8.0). What is the length of MN, denoted as variable x, in relation to u, v, and w?\nLet's think step by step and output the final... | MATH | {
"ground_truth": "6",
"style": "rule"
} | {
"difficulty": "1",
"index": "07e8ec4e-83f2-4435-80fa-6480bff9fdf8"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a triangle VKY. The measure of angle KVY is 67 degrees. What is the sum of the measures of angles KYV and VKY?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "113 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "a2a7d7aa-5b34-458b-aebf-387b3e8607ec"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle X with lines XR, XS, XU, XW, XQ. Which lines are equal in length to line XR?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "XS, XU, XW, XQ",
"style": "rule"
} | {
"difficulty": "1",
"index": "cf889435-a512-4233-8ad5-ee3505feba35"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, let the distance between AB and CD be represented by the variable 'y'. If AB is parallel to CD, OA and OC bisect angle BAC and angle ACD respectively, OE is perpendicular to AC at point E, and OE = 2.0, what is the value of 'y' in relation to OE?\nLet's think step by st... | MATH | {
"ground_truth": "4",
"style": "rule"
} | {
"difficulty": "1",
"index": "b51754e5-b2cb-449f-943d-f4bc7b16aa6f"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given diagram, equilateral triangle DEF is obtained by translating equilateral triangle ABC along the direction of ray BC. If AB is 12 units long and EC is 4 units long, what is the length of BF?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "u... | MATH | {
"ground_truth": "20.0",
"style": "rule"
} | {
"difficulty": "1",
"index": "d5068270-9529-4ea7-9b78-662fa95dc821"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle D. There are lines DS, BC, UP in the diagram. Point S, Point B, Point C, Point U, and Point P lie on the circle D. Which lines are equal in length to line DS?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "DB, DC, DU, DP",
"style": "rule"
} | {
"difficulty": "1",
"index": "cef9d067-8be5-445d-8c0c-bed328e8f7ea"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, if the measure of angle DCB is 'a' (a = 90.0 degrees), and the sum of angle 2 and angle B is 'b' (b = 70.0 degrees), what is the degree measure of angle 1, expressed as 'c' in terms of 'a' and 'b'?\nLet's think step by step and output the final answer within \\boxed{}."... | MATH | {
"ground_truth": "20°",
"style": "rule"
} | {
"difficulty": "1",
"index": "00de1057-feaa-4c76-85e4-dbe134b63721"
} | |
multimodal_opensource_math | [
{
"content": "<image>Find the value of \\( x \\) and then determine the length of \\( RT \\)\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "8",
"style": "rule"
} | {
"difficulty": "1",
"index": "de23f223-757a-42c5-91b3-44812fa847b6"
} | |
multimodal_opensource_math | [
{
"content": "<image>The diagrams provided illustrate the transformation of a cup filled with liquid from Figure 1 to Figure 2. What is the measurable value of the liquid level AB in the second figure, after a certain amount of liquid is removed from the cup?\nLet's think step by step and output the final answe... | MATH | {
"ground_truth": "3cm",
"style": "rule"
} | {
"difficulty": "1",
"index": "86aba2bc-127a-43ee-a027-b0f1d5135577"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a pentagon in the diagram, represented by the symbol HCYUX. The measure of angle XHC is equal to 90 degrees. The measure of angle HCY is equal to 90 degrees. What kind of pentagon is HCYUX?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"... | MATH | {
"ground_truth": "a right-angled pentagon",
"style": "rule"
} | {
"difficulty": "1",
"index": "3de3fa85-a3b4-41cb-8c5f-40b0a5587e11"
} | |
multimodal_opensource_math | [
{
"content": "<image>If x = 3, what is the length of the side labeled (10/3)x + 4?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "14",
"style": "rule"
} | {
"difficulty": "1",
"index": "b2096606-a864-4c0f-9f66-1c48acd0df98"
} | |
multimodal_opensource_math | [
{
"content": "<image>如图,在△ABC中,∠ABC=45°,AC=8cm,F是高AD和BE的交点,则BF的长是()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "8cm",
"style": "rule"
} | {
"difficulty": "1",
"index": "17b232a9-1a84-4a59-897a-ff727ccb5f74"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a trapezoid in the diagram, represented by the symbol VQRB. Line BN is the extension line of line RB. What is the relationship between point B, point R, and point N?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "R, B, N are collinear",
"style": "rule"
} | {
"difficulty": "1",
"index": "84394087-e750-45ff-aac7-fcb15d7e4344"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given diagram, AB is parallel to CD. The intersection of AF and CD is point E, and BE is perpendicular to AF at E. If angle BED measures 35°, what is the degree measure of angle A?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "55°",
"style": "rule"
} | {
"difficulty": "1",
"index": "9e1bd552-9fca-487c-9239-69e3fc5e0789"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the combined degree measurement of angles 1 and 2 if angle A in triangle ABC measures 50 degrees?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "230°",
"style": "rule"
} | {
"difficulty": "1",
"index": "1cc83bd6-4a62-4808-9eff-d73226ea301d"
} | |
multimodal_opensource_math | [
{
"content": "<image>If AC is the diameter of circle O and there is a chord AB that runs parallel to CD, what is the measure of angle AOD if angle BAC is 32.0 degrees?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "64°",
"style": "rule"
} | {
"difficulty": "1",
"index": "11e162f2-cd63-4d42-9ed3-8ab8c82d4e43"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given that AB is the diameter of circle O and chord CD is perpendicular to AB at point E, and the length of CD is 2 times the length of OE, what is the size of angle BCD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "22.5°",
"style": "rule"
} | {
"difficulty": "1",
"index": "7812d525-51bb-4403-991f-33aa08b353ec"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a trapezoid in the diagram, represented by the symbol ATUR. Line AT is parallel to line UH. The length of line RA is 5. What is the length of line AR?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "5",
"style": "rule"
} | {
"difficulty": "1",
"index": "1a2de822-68c3-4597-acfe-29b4ea58d308"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle V. ['D', 'Q', 'K', 'Z', 'I'] are points on the circle V. Which lines are equal in length to line VD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "VQ, VK, VZ, VI",
"style": "rule"
} | {
"difficulty": "1",
"index": "94de120d-7fc4-417b-be79-34bd43a3e685"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the perimeter of the parallelogram NQRM?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "58",
"style": "rule"
} | {
"difficulty": "1",
"index": "a32aa90f-7760-4347-a0dc-b6fdd883ed6a"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given diagram, let's denote the length of AC as variable h (h = 8) and the length of AD as variable k (k = 5). If quadrilateral ABCD is a rhombus and DH is perpendicular to AB at point H, what is the length of DH, represented as variable n in terms of h and k?\nLet's think step by st... | MATH | {
"ground_truth": "4.8",
"style": "rule"
} | {
"difficulty": "1",
"index": "6d34ee17-f3f0-45c7-89c8-5bd18570f58c"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, let O be the center of the circle and AD be the diameter. If arc AB is equal in measure to arc CD and angle AOB equals 40.0 degrees, what is the measure of angle BPC formed on the circumference?\nLet's think step by step and output the final answer within \\boxed{}.",
... | MATH | {
"ground_truth": "50°",
"style": "rule"
} | {
"difficulty": "1",
"index": "7e54ffd8-714f-440d-8801-c8fc4091ea14"
} | |
multimodal_opensource_math | [
{
"content": "<image>如图，PB为圆的切线，B为切点，连接PO交圆于点A，PA=2，PO=5，则PB的长为()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "4",
"style": "rule"
} | {
"difficulty": "1",
"index": "ce11f1a5-c57c-4d96-93b0-ed01e14d55cf"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the circle is to be divided into four equal parts by drawing two lines from the center O to the circumference, what will be the length of each arc created?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "5π cm",
"style": "rule"
} | {
"difficulty": "1",
"index": "bd1f5621-5772-4667-a829-6ca9c8415961"
} | |
multimodal_opensource_math | [
{
"content": "<image>How many sides does a hexagon have?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "A hexagon has 6 sides",
"style": "rule"
} | {
"difficulty": "1",
"index": "4da426c5-208f-4e7d-b4e3-ceadf731622f"
} | |
multimodal_opensource_math | [
{
"content": "<image>In triangle PQR, with DE being parallel to QR, if PD=p, DR=r, and DE=d, express the length of QR in terms of p, r, and d\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "9",
"style": "rule"
} | {
"difficulty": "1",
"index": "c6e52b86-66cc-4dc9-901b-700099ae1fd0"
} | |
multimodal_opensource_math | [
{
"content": "<image>The derivative of f(x) at x=1 is ____ that at x=0\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "equal to",
"style": "rule"
} | {
"difficulty": "1",
"index": "b76e45e7-f8f4-45ab-8bfc-7506229b5cf9"
} | |
multimodal_opensource_math | [
{
"content": "<image>Line BW is perpendicular to line QG. Point W lies on line QG. What is the measure of angle BWQ?\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": "cf5ca551-9b68-41f9-8602-84ec31e1417a"
} | |
multimodal_opensource_math | [
{
"content": "<image>Assuming angle 1 and angle 2 both measure 145 degrees in the diagram, what is the measure of angle 3?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "70°",
"style": "rule"
} | {
"difficulty": "1",
"index": "566e450f-977a-4417-8f90-cca818cfd0bb"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a rhombus in the diagram, represented by the symbol ADHP. The length of line DH is 6. What is the length of line AD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "6",
"style": "rule"
} | {
"difficulty": "1",
"index": "978cf8cd-9bdf-4ca7-921a-115a3af6b12c"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a triangle KMC. Which three points are collinear?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "V, J, and U",
"style": "rule"
} | {
"difficulty": "1",
"index": "3507b173-bde9-41b8-bb3a-4ab07bf78b36"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, the height of the street lamp AB measures 8.0 units. The tree CD is located at a horizontal distance of 4.0 units from the street lamp. If the shadow length of the tree under the light DE is 3.0 units, what is the height of the tree?\nLet's think step by step and out... | MATH | {
"ground_truth": "\\frac{24}{7}米",
"style": "rule"
} | {
"difficulty": "1",
"index": "db0a1583-cc49-4222-ac9d-e7798d27e451"
} | |
multimodal_opensource_math | [
{
"content": "<image>Let AB be a line segment with a length of 'L' units. If point C lies on the line segment AB, and the midpoints of AC and CB are D and E respectively, how can the length of DE be expressed in terms of 'L'?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": ... | MATH | {
"ground_truth": "5cm",
"style": "rule"
} | {
"difficulty": "1",
"index": "8cba02c9-012c-43f7-9532-9db72157f879"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given triangle ABC with AD as the altitude and AE as the angle bisector of BAC, and with angle B measuring 50 degrees and angle C measuring 80 degrees, what is the measure of angle DAE?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "15°",
"style": "rule"
} | {
"difficulty": "1",
"index": "3df9ba0e-5ea3-4143-959e-c97f42709b13"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given diagram, if AB is parallel to DE and angle ABC is denoted by variable p (p = 70.0 degrees) and angle CDE is denoted by variable q (q = 140.0 degrees), what is the value of angle BCD, expressed as variable r in terms of p and q?\nLet's think step by step and output the final ans... | MATH | {
"ground_truth": "30°",
"style": "rule"
} | {
"difficulty": "1",
"index": "f567cd25-d388-4f61-a830-79e8160ef2a3"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, angle A is the angle of circumferential of circle O, angle A = 50.0, then the degree of angle OBC is ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "40°",
"style": "rule"
} | {
"difficulty": "1",
"index": "7d867370-829d-45ce-bbf1-6b07e43310d1"
} | |
multimodal_opensource_math | [
{
"content": "<image>When the plant spacing between two trees on a hilledge with a slope ratio of i=1:frac{m}{n} is 4.0, what is the expression for the slope distance between two adjacent trees in terms of the vertical height 'z'?\nLet's think step by step and output the final answer within \\boxed{}.",
"ro... | MATH | {
"ground_truth": "5m",
"style": "rule"
} | {
"difficulty": "1",
"index": "8a757c89-eca1-46ad-91c5-90457afe165e"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the ABCDE shape is a combination of a rectangle and an equilateral triangle and the perimeter of the ABCDE shape is 54, compute the length of the AB side of the ABCDE shape. Round computations to 2 decimal places.\nLet's think step by step and output the final answer within \\boxed{}.",
... | MATH | {
"ground_truth": "16.5",
"style": "rule"
} | {
"difficulty": "1",
"index": "b0eafeb4-8160-46bd-b77a-4f3071fe780c"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, the line FO intersects the line QL at point D. What is the length of QD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "1.98",
"style": "rule"
} | {
"difficulty": "1",
"index": "5db40b7d-742c-4881-9cf4-bedbf89b60da"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, the vertices A, B, and C of triangle ABC are all on circle O, if angle ABC = 28.0, then the size of angle AOC is ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "56°",
"style": "rule"
} | {
"difficulty": "1",
"index": "1053ae33-7144-4a59-a79b-5fabeb3bbccd"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given a parallelogram ABCD, where the side lengths are AB = m units, AD = n units, and AC forms a right angle with BC, what is the formula for the area of ABCD based on m and n?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "60",
"style": "rule"
} | {
"difficulty": "1",
"index": "263af3d8-4a3c-40d7-b489-4ec0d0275655"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the area of the yellow sector is 127.17, compute the degree of the angle marked with question mark. 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": "86.4",
"style": "rule"
} | {
"difficulty": "1",
"index": "dd9c0a9e-76b2-4761-9f18-1f49be1a49d5"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the area of the magenta sector is 157, the red shape is a combination of a rectangle and a semi-circle, the perimeter of the red shape is 56 and the area of the orange square is 64, compute the degree of the angle marked with question mark. Assume $\\pi=3.14$. Round computations to 2 dec... | MATH | {
"ground_truth": "57.6",
"style": "rule"
} | {
"difficulty": "1",
"index": "dde3d09f-7b27-40c8-9f76-15e23885fd18"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the arc length of the purple sector is 17.99, the arc length of the brown sector is 17.99, the magenta shape is a rectangle where an equilateral triangle has been removed from one side of it, the area of the magenta shape is 120 and the angle $\\alpha$ is vertical to $\\beta$, compute th... | MATH | {
"ground_truth": "15.92",
"style": "rule"
} | {
"difficulty": "1",
"index": "a85760be-5d70-4b76-99be-92251349578e"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a triangle LVB. The measure of angle VLB is equal to 60 degrees. What is the sum of the measures of the other two angles?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "120 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "96dea16a-2c5f-475c-9172-567db21e6f67"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given depiction, if the ratio of the segments AB to AD is given by p:q, and the discrepancy between the perimeters of triangles AOB and AOD is specified as d, calculate the perimeter of the parallelogram ABCD\nLet's think step by step and output the final answer within \\boxed{}.",
... | MATH | {
"ground_truth": "30",
"style": "rule"
} | {
"difficulty": "1",
"index": "21dc4eb1-cea2-420c-99d2-405015bca65f"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the figure provided, a parallelogram ABCD is illustrated, and it is given that AE bisects angle BAD, intersecting the DC edge at point E. DF is perpendicular to AE at F, and the measure of angle ADF is 50.0 degrees. What is the degree measure of angle C?\nLet's think step by step and out... | MATH | {
"ground_truth": "80°",
"style": "rule"
} | {
"difficulty": "1",
"index": "36b55c22-7d2e-4ed6-b208-b7f6c81e1adc"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, if the angle AOC is represented by the variable h where h = 116°, what is the degree measure of angle ADC, 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": "122°",
"style": "rule"
} | {
"difficulty": "1",
"index": "4a153f75-923f-4b06-9a71-8a93a9499756"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the depicted figure, with the right angle vertex A of the set square placed on the line DE and BC set parallel to DE, what is the expression for angle DAC in terms of 'x', where angle B = x?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
... | MATH | {
"ground_truth": "120°",
"style": "rule"
} | {
"difficulty": "1",
"index": "36aa7ec8-2b87-4d8a-be06-59fcba5f0685"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the total number of objects in the image?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "7",
"style": "rule"
} | {
"difficulty": "1",
"index": "a33b3a26-37eb-45f9-a293-df2c126eceaa"
} | |
multimodal_opensource_math | [
{
"content": "<image>Matrices A, B, and C are given in the image. What is the trace of the matrix (A - B - C)?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "-3",
"style": "rule"
} | {
"difficulty": "1",
"index": "0eb7988e-b776-4b03-a285-d8da7d736f47"
} | |
multimodal_opensource_math | [
{
"content": "<image>How many objects are matte in texture?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "3",
"style": "rule"
} | {
"difficulty": "1",
"index": "0abe4d07-0a80-49a0-9061-addee7c4e042"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, in triangle ABC, angle B = 38°, angle C = 54°, AE is the altitude on side BC, and AD is the bisector of angle BAC. The degree of angle DAE is ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "8°",
"style": "rule"
} | {
"difficulty": "1",
"index": "9c507ae2-6eae-4d29-9d43-44a421d42042"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle O. The measure of the central angle WHI is 31 degrees. What is the degree of the arc formed by points W and I on circle O?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "62 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "eb101c25-cc7a-42cc-97bd-940b8b3ae9c1"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle O with a radius of 0.6. If the measure of the angle YOF is 23 degrees, what is the measure of the angle FOY?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "157 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "47293cc7-afa7-48ef-a2f6-9611f0ae2aac"
} | |
multimodal_opensource_math | [
{
"content": "<image>In triangle ABC, the points D and E are on the edges AB and AC respectively, DE parallel BC. If AE/AC = 3/4 and AD = 24, then what is the length of AB?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "32.0",
"style": "rule"
} | {
"difficulty": "1",
"index": "1407f88b-9ae3-4b8c-80d2-e7b424339307"
} | |
multimodal_opensource_math | [
{
"content": "<image>How many cylinders are there in the image?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "2",
"style": "rule"
} | {
"difficulty": "1",
"index": "88c7f7c6-d4fb-443f-847f-3819b47615fb"
} | |
multimodal_opensource_math | [
{
"content": "<image>Determine the value of x, assuming that segments that seem to be tangent are indeed tangent.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "3",
"style": "rule"
} | {
"difficulty": "1",
"index": "a917203a-8e66-4687-896f-ff927cd180bb"
} | |
multimodal_opensource_math | [
{
"content": "<image>If AB is the diameter of circle O and angle E is 40 degrees, what is the length of chord AC if the radius of the circle is 5 cm?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "2 * 5 / sin(40)",
"style": "rule"
} | {
"difficulty": "1",
"index": "682fabd0-d610-4f1d-85bf-5675dfce0f14"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the rectangle ABCD, given that the diagonals AC and BD intersect at point O and AE is the perpendicular bisector of BO, if AE is equal to 20 units, what is the length of OD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "40.0",
"style": "rule"
} | {
"difficulty": "1",
"index": "484ab9fa-bd6a-41e6-9685-4920e69cc99f"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, if AB represents the diameter of circle O, CD is a chord of circle O, angle C is denoted by the variable 'x' (x = 30.0), and BD is represented by the variable 'y' (y = 1.0), what is the radius of circle O? Express the radius as 'r' in terms of 'y'\nLet's think step by s... | MATH | {
"ground_truth": "1",
"style": "rule"
} | {
"difficulty": "1",
"index": "a9d6629a-8d5c-464c-a8d3-d5e1edc0eadf"
} | |
multimodal_opensource_math | [
{
"content": "<image>If angle 1 is established as 60.0 degrees in the figure where paper strips are placed parallel to the two edges of a right angle triangle, what will be the degree measure of angle 2?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "30°",
"style": "rule"
} | {
"difficulty": "1",
"index": "29f3795a-4ca8-4e4d-bf50-5d0186c37ade"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle O with a radius of 1.5. The measure of the angle FOZ is 51 degrees. What is the length of the arc FZ?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "1.34\\pi",
"style": "rule"
} | {
"difficulty": "1",
"index": "75e3273e-8732-48c0-843c-c9522b0d7893"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given scenario with a wire rope fixing rod BC, the angle between the wire rope and the ground is represented as 'θ' (θ = 30.0°), and the height of BC is 'h' units (h = 18.0). Determine the length of the wire rope AC. Express the length as 'x' units\nLet's think step by step and outpu... | MATH | {
"ground_truth": "36米",
"style": "rule"
} | {
"difficulty": "1",
"index": "40fc8b1f-297c-42f1-8585-b92a4cd8525c"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the figure, in triangle ABC, points D and E are the midpoints of sides BC and BA respectively. If the area of triangle ABC is 32, then the area of triangle DEB is ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "8",
"style": "rule"
} | {
"difficulty": "1",
"index": "57a73425-ec65-4ab6-96d4-565ab26314e1"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a right triangle in the diagram, represented by the symbol PYU. The measure of angle UPY is equal to 90 degrees. What is the sum of the measures of angles YPU and PUY?\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": "1b5e82ba-26ba-4f65-b817-000f86a0f487"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given diagram, AB is parallel to CD, angle EBF is equal to angle FBA, angle EDG is equal to angle GDC, and angle E measures 45°. What is the measure of angle H?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "22.5°",
"style": "rule"
} | {
"difficulty": "1",
"index": "8ba3134d-39a9-4f1c-ac80-0860070863e6"
} | |
multimodal_opensource_math | [
{
"content": "<image>Find the measure of \\angle 7 if A B \\perp B C.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "140",
"style": "rule"
} | {
"difficulty": "1",
"index": "06c3373a-fc47-4947-bdf4-14cf8e8cb1e7"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the measure of angle EPM?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "114 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "10279b9e-6c5c-48f5-9d56-900645e2acaf"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram provided, circle O is tangent to lines PA and PB at points A and B, with angle APB measuring 60 degrees. If the length of PO is given as 4, what is the radius of circle O?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "2",
"style": "rule"
} | {
"difficulty": "1",
"index": "dbb1ce9f-5e00-4723-8918-e939c0a5957a"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle B. The line CK is a chord of the circle and is perpendicular to the radius BD at point Z, with BZ=1.3. What is the angle BZD?\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": "b7c029ac-c8fb-4d5e-9d52-4c749990534b"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a parallelogram in the diagram, represented by the symbol MUEX. What is the length of line EX?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "9",
"style": "rule"
} | {
"difficulty": "1",
"index": "d5899e18-4e5c-4e17-8738-c7e27a228761"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given the diagram illustrating circle O with AB as its diameter, and point C lying on circle O (excluding points A and B), if angle BOD is determined to be 44.0 degrees, what is the degree measurement of angle C?\nLet's think step by step and output the final answer within \\boxed{}.",
... | MATH | {
"ground_truth": "22°",
"style": "rule"
} | {
"difficulty": "1",
"index": "fbda8dce-6555-4e2c-8287-a0f1d58f9c86"
} | |
multimodal_opensource_math | [
{
"content": "<image>In triangle ABC, let's denote angle B as variable 'm' and angle C as variable 'n' where m = n = 50.0 degrees. If BD is equal to CF and BE is equal to CD, what is the numerical value of angle EDF, expressed as variable 'p' in relation to 'm' and 'n'?\nLet's think step by step and output the ... | MATH | {
"ground_truth": "50°",
"style": "rule"
} | {
"difficulty": "1",
"index": "75f43aad-f2ee-4af8-934c-139ecdc10ccd"
} | |
multimodal_opensource_math | [
{
"content": "<image>In parallelogram ABCD, given that AC and BD intersect at point O, angle BAC is 90 degrees, point E is the midpoint of BC, AE is 7 units long, and the perimeter of triangle AOD is 3 units more than the perimeter of triangle AOB, what is the perimeter of parallelogram ABCD?\nLet's think step ... | MATH | {
"ground_truth": "44.0",
"style": "rule"
} | {
"difficulty": "1",
"index": "5551acc6-79ea-46fc-8c02-f0cbd5110e5d"
} | |
multimodal_opensource_math | [
{
"content": "<image>If AB is the diameter of circle O and AB is perpendicular to DE at point Q, what is the measure of angle AED?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "180 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "b8f51579-363e-41f1-8f23-a1181f4602c6"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle B. Points D, C, J, I lie on the circle B. Which lines are equal in length to line BD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "CD, BJ, BI",
"style": "rule"
} | {
"difficulty": "1",
"index": "29448688-1726-499f-ae7e-89ba7a1810be"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle J with points Z, Q, F, Y, and I lying on its circumference. Which lines are equal in length to line JZ?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "JQ, JF, JY, and JI",
"style": "rule"
} | {
"difficulty": "1",
"index": "cce9a654-9f5d-4ade-a693-dfe9c5a9c855"
} | |
multimodal_opensource_math | [
{
"content": "<image>Find the measure of \\angle 8 if A B \\perp B C.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "14",
"style": "rule"
} | {
"difficulty": "1",
"index": "41336922-008a-4cd7-8248-9602c9942966"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram where C is a point on the arc AB, if angle AOB is measured at 120°, what is the degree measure of angle ACB?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "120°",
"style": "rule"
} | {
"difficulty": "1",
"index": "726c2d72-0515-4188-94ae-8454eee786aa"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, let's denote the height of the tree as variable h. If the tree is divided into three segments at heights of 3m and 5m above the ground, and the top of the tree falls 6m away from the bottom, what is the value of h in terms of other variables?\nLet's think step by step a... | MATH | {
"ground_truth": "10m",
"style": "rule"
} | {
"difficulty": "1",
"index": "af80d8d0-f13b-42d3-87b0-8ccc855f0128"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given illustration of circle O, the perpendicular radius of AO is connected to OB. Point P is located on the major arc APB and C is the midpoint of AB. What is the degree measure of angle APC after connecting AP and CP?\nLet's think step by step and output the final answer within \\b... | MATH | {
"ground_truth": "22.5°",
"style": "rule"
} | {
"difficulty": "1",
"index": "e2c67dab-d740-4136-9953-aecb464f89b3"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the figure, point E is the midpoint of side CD of quadrilateral ABCD, the extension of AD and BE intersect at point F, DF = 3, DE = 2, what is the perimeter of quadrilateral ABCD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "14",
"style": "rule"
} | {
"difficulty": "1",
"index": "9fbdaa07-055e-4902-87fb-85da03b7bd3b"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the provided figure, circle O contains points A, B, and C. If angle AOB measures 72.0 degrees, what is the degree measure of angle ACB?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "36°",
"style": "rule"
} | {
"difficulty": "1",
"index": "c2b50ea5-4413-4cb8-bd1f-f3f840a5a012"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the arc length of the ABC sector is 20.56 and the area of the pink semi-circle is 100.48, compute the degree of the CBA angle. 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": "72",
"style": "rule"
} | {
"difficulty": "1",
"index": "648a29e2-77c0-4dcd-b2b6-7d097c39f7ac"
} | |
multimodal_opensource_math | [
{
"content": "<image>Let triangle ABC be inscribed in circle O, whereby the vertices A, B, and C lie on the circle. If the measure of angle OAC is 'm' and the measure of angle OBC is 'n', what is the degree of angle AOB? Express the solution in terms of 'm' and 'n'\nLet's think step by step and output the final... | MATH | {
"ground_truth": "110°",
"style": "rule"
} | {
"difficulty": "1",
"index": "1719fd6d-6553-4747-b0be-c6c8f2aefda1"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given a standard eye chart with a reference test distance of 'D_initial' units and a specific measurement 'M_initial' for the letter \"E\", construct a new eye chart with a modified test distance of 'D_modified' units. Determine the resulting measurement 'M_modified' of the letter \"E\" in ... | MATH | {
"ground_truth": "2.16cm",
"style": "rule"
} | {
"difficulty": "1",
"index": "74b2c888-e0ef-4571-9936-93b044d278c5"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the length of segment DT if DE = 7 and EX = 24?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "17",
"style": "rule"
} | {
"difficulty": "1",
"index": "b676e1dd-b935-48ad-aa75-be8f2f052e4e"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a triangle XJK. The measure of angle JXK is equal to 85 degrees. What is the sum of the measures of angles XJK and KJX?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "95 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "797e6017-fe50-42fd-893e-430a8ad7145e"
} | |
multimodal_opensource_math | [
{
"content": "<image>When the two triangles in the figure are congruent, what is the measurement of angle α?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "70°",
"style": "rule"
} | {
"difficulty": "1",
"index": "eba1f627-1109-4eff-80b5-65ab2cd50f5c"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the measure of angle 2 in the given diagram, where angle A is 30 degrees and angle 1 is 39 degrees, and the right-angled vertex of a triangle plate is placed on one of two mutually parallel lines?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": ... | MATH | {
"ground_truth": "21°",
"style": "rule"
} | {
"difficulty": "1",
"index": "59d2618f-9fd1-4e5a-a376-c4bc362acfc6"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, in parallelogram ABCD, if the sum of angles A and C is 130 degrees, what would be the measurement of angle B?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "115°",
"style": "rule"
} | {
"difficulty": "1",
"index": "31e18a5f-9112-45fc-a4d3-c29922c7f04a"
} | |
multimodal_opensource_math | [
{
"content": "<image>If AC = DC = DB and angle ACD is 48 degrees, what is the length of AD if BD is 10 units?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "10 * sqrt(2) units",
"style": "rule"
} | {
"difficulty": "1",
"index": "4f9cf7d4-2a74-43ea-93e8-ea07d890e8a2"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, AD is the median of triangle ABC. E is the midpoint of AD. If the area of triangle ABE is 2, then the area of triangle ABC is ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "8",
"style": "rule"
} | {
"difficulty": "1",
"index": "ba2a40ae-5c25-4e01-a0a6-02ee9814f7f5"
} |
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