prob_id stringlengths 6 9 | image imagewidth (px) 139 1.6k | problem stringlengths 87 281 | solution stringlengths 66 566 |
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prob_0 | Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AC \perp EB on B, ED = AC = 15, AE = DC = 13, AB = 7. Solve the problem: Gougu V0 7 13 Para_Area 15 V0 V1 Get V1. | |
prob_1 | Line m is the perpendicular bisector of XZ, WZ = 14.9. Find WX. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: line m \perp XZ on Y, XY = YZ. Solve the problem: Equal 14.9 V0 Get V0. | |
prob_2 | Polygon BCDE \cong polygon RSTU. Find z. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: BC = 4w-7, TU = z+16, DE = 3z+10, RS = 2w+13, UR = 12, CD = 11, m \angle EDC = 2y-31, m \angle UTS = y+11, m \angle EBC = 2x+9, m \angle URS = 49. Solve the problem: Equal z+16 3z+10 Get z. | |
prob_3 | Find x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AB \perp CA on A, CA = 22, AB = 20, BC = x. Solve the problem: Gougu 22 20 x Get x. | |
prob_4 | Find the length of DB. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: CD = 9, CB = CD = x+3, AB = 7y-2, DA = 30. Solve the problem: Multiple 9 2 V0 Get V0. | |
prob_5 | Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: DE \perp AD on D, BC \perp CF on C, m \angle BAD = m \angle EFC = x, m \angle ABC = m \angle DEF = x+22. Solve the problem: Ngon_Angsum 6 V0 Sum x x x+22 x+22 90 90 V0 Get x. | |
prob_6 | Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle DCB = 70, m \angle BDC = 4x, m \angle ABC = 10x+22. Solve the problem: Sum 70 4x 10x+22 Get x. | |
prob_7 | Find x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: ST = 12+x, SR = 4x-4, RT = SR = 3x+3. Solve the problem: Equal 4x-4 3x+3 Get x. | |
prob_8 | Find the perimeter of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AB \perp CE on C, CE = 7. Solve the problem: RNgon_H_Area 6 7 V0 RNgon_B_Area 6 V1 V0 Multiple V1 6 V2 Get V2. | |
prob_9 | For isosceles trapezoid ABCD, X and Y are midpoints of the legs. Find m \angle A if m \angle ADY = 78. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle YDA = 78. Solve the problem: Equal 78 V0 Get V0. | |
prob_10 | Find the value of variable y. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle ABD = x, m \angle DFE = y, m \widehat AE = 72. Solve the problem: Multiple y 2 72 Get y. | |
prob_11 | Find the measurement of BC. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AD = 3\frac{3}{4}, AB = BC = CD. Solve the problem: Multiple V0 3 3\frac{3}{4} Get V0. | |
prob_12 | Find y. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: DC \perp AD on D, AC \perp DB on B, CB = 4, AB = 12, AD = x, CD = z, BD = y. Solve the problem: Geo_Mean 12 4 y Get y. | |
prob_14 | Solve for m \angle YBX. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: BY = 75, BX = 30, YX = 60. Solve the problem: Cos_Law 60 75 30 V0 Get V0. | |
prob_15 | Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: CD \perp AB on B, AB = 8, DC = 21. Solve the problem: Tria_BH_Area 21 8 V0 Get V0. | |
prob_16 | Find x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: PR \perp QR on R, QP = 4, QR = RP = x, m \angle QPR = 45. Solve the problem: Gougu x x 4 Get x. | |
prob_17 | If c = 5, find b. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: CA \perp BC on C, BA = c, BC = a, AC = b, m \angle ABC = 60, m \angle BAC = 30. Solve the problem: Equal c 5 Gsin b c 60 Get b. | |
prob_18 | Find the value of x that makes line r \parallel line s. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle HFE = x, m \angle ABC = 90-x. Solve the problem: Equal x 90-x Get x. | |
prob_19 | Find the length of \widehat XW. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: YZ = 12, m \widehat XW = 55. Solve the problem: Circle_R_Circum 12 55 V0 Get V0. | |
prob_20 | In \triangle PQR, ST \parallel RQ. If PS = 12.5, SR = 5, and PT = 15, find PQ. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: ST \parallel RQ. Solve the problem: Proportion 12.5 5 15 V0 Sum 15 V0 V1 Get V1. | |
prob_21 | Find m \angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: BC \perp GD on G, AD \perp BF on F, CD \perp BD on D, m \angle BDF = 28, m \angle BEF = 51, m \angle BAE = 25, m \angle DBG = 35, m \angle DCG = m \angle 4, m \angle EBA = m \angle 3, m \angle CDG = m \angle 6, m \angle EBF = m \angle 2, m \angle BDG = m \angle 5, m \angle DBF = m \angle 1. S... | |
prob_22 | Find m \widehat BA. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AQ = 10, m \angle AQB = 120. Solve the problem: Equal V0 120 Get V0. | |
prob_23 | Find the perimeter of circle. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: CD = 1.5, m \widehat BA = 160. Solve the problem: Multiple 1.5 2 V0 Get V0. | |
prob_24 | For trapezoid QRST, A and B are midpoints of the legs. Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: TS = 12, QR = 20, m \angle STA = 120, m \angle BRQ = 45. Solve the problem: Median 12 V0 20 Get V0. | |
prob_25 | In \odot P, RT = 11, find m \widehat QTS. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle SPR = 130, m \angle QPT = 112. Solve the problem: Sum 130 V0 180 Sum 112 V0 V1 Get V1. | |
prob_26 | If x = 7\sqrt{3}, find y. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: BA \perp EC on E, BC \perp CA on C, BC = a, CA = b, BE = x, AE = y, BA = c, m \angle EAC = 30, m \angle EBC = 60. Solve the problem: Equal x 7\sqrt{3} Gtan V0 x 60 Gtan V0 y 30 Get y. | |
prob_28 | WXYZ is a parallelogram. Find m \angle XWZ. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle AXY = 33, m \angle WXA = 82. Solve the problem: Sum 33 82 V0 Sum V0 V1 180 Get V1. | |
prob_29 | What is the area of trapezoid EFGH? Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: EH \parallel FG, EH \perp FJ on J, GF = 8, FJ = 4, HE = 13. Solve the problem: Trap_Area 8 13 4 V0 Get V0. | |
prob_30 | m \angle SXT = 3a-4, m \angle RXS = 2a+5, m \angle RXT = 111, find m \angle RXS. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: . Solve the problem: Sum 3a-4 2a+5 111 Get 2a+5. | |
prob_32 | In rhombus QRST, m \angle TSR = 2 m \angle QRS and TS = 15. Find QR. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: . Solve the problem: Equal 15 V0 Get V0. | |
prob_33 | Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AD \perp CD on D, AC \perp BD on B, CD = y, DB = x, AC = 50, BA = 40. Solve the problem: Sum 40 V0 50 Geo_Mean 40 V0 x Get x. | |
prob_34 | Find m \widehat JLM. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle LBJ = 47, m \widehat JL = 111. Solve the problem: TanSec_Ang 47 111 V0 Sum V0 V1 360 Get V1. | |
prob_35 | WXYZ is a square. If WT = 3, find ZX. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: XW \perp XY on X, YZ \perp XY on Y, YZ \perp WZ on Z, WZ \perp XW on W. Solve the problem: Multiple 3 2 V0 Get V0. | |
prob_36 | What is the measure of \angle 2? Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle CDE = 38, m \angle BAC = m \angle 2, m \widehat BA = 70. Solve the problem: Equal 38 V0 Get V0. | |
prob_37 | Find the perimeter of the polygon. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AB \perp AC on A, AB \perp BD on B, CD \perp AC on C, CD \perp BD on D, BD = 5, CD = 9. Solve the problem: PRK_Perim 5 9 V0 Get V0. | |
prob_38 | Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: BC \perp DB on B, m \angle CBA = 110, m \angle ABE = x, m \angle EBD = 30. Solve the problem: Sum 110 x 30 90 360 Get x. | |
prob_39 | JKLM is a rhombus. If CK = 8, JK = 10 and \angle JKM = 37. What is m \angle MLJ? Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: . Solve the problem: Sum 37 V0 90 Equal V0 V1 Get V1. | |
prob_40 | Quadrilateral DEFG is a rectangle. If m \angle EFD = 2x-3 and m \angle DFG = x+12, find m \angle EFD. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: GF \perp DG on G. Solve the problem: Sum 2x-3 x+12 90 Get 2x-3. | |
prob_41 | What is the circumference? Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AC = 12\frac{1}{2}. Solve the problem: Circle_R_Circum 12\frac{1}{2} V0 Get V0. | |
prob_42 | The angle bisectors of \triangle XYZ meet at point W. What is the measure of \angle ZXY? Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: ZY \perp BW on B, ZX \perp AW on A, XY \perp WC on C, CW = 20, WX = 75. Solve the problem: Gsin 20 75 V0 Multiple V0 2 V1 Get V1. | |
prob_43 | Find CD. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: BD \perp AC on E, DE = 5, EC = 12, AB = AD, DC = BC. Solve the problem: Gougu 5 12 V0 Get V0. | |
prob_44 | \triangle ABC is an isosceles triangle with base BC. What is the perimeter of the triangle? Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: BA = 2x+4, BC = 4(x-2), AC = 3x-1. Solve the problem: Equal 2x+4 3x-1 Sum 2x+4 4(x-2) 3x-1 V0 Get V0. | |
prob_45 | Find the measure of \angle B. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AB = 13, AC = 12, CB = 15. Solve the problem: Cos_Law 12 13 15 V0 Get V0. | |
prob_47 | For trapezoid QRST, M and P are midpoints of the legs. If TS = 2x, PM = 20, and QR = 6x, find x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: . Solve the problem: Median 2x 20 6x Get x. | |
prob_48 | Find x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AN \parallel DO \parallel FP, EC = 17+5y, EG = 13+6y, KL = 3x-9, KJ = LK = 4x-22. Solve the problem: Equal 3x-9 4x-22 Get x. | |
prob_49 | Find the perimeter of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AB = 4. Solve the problem: RNgon_L_Area 3 4 V0 RNgon_B_Area 3 V1 V0 Multiple V1 3 V2 Get V2. | |
prob_50 | KN and JL are diameters. Solve for m \widehat JML. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle NQM = 55, m \angle KQL = 60. Solve the problem: Equal V0 180 Get V0. | |
prob_51 | Find m \angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: IF \parallel CA, m \angle HGF = 157, m \angle DEG = 90, m \angle ADB = m \angle 1. Solve the problem: Sum V0 V1 180 Sum 157 V2 180 Sum V1 V2 90 Get V0. | |
prob_52 | If \angle ACB is a right angle, m \angle 1 = 4y, and m \angle 2 = 2y+18, find m \angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AD = x+8, BD = 2x+5, m \angle ACD = m \angle 1, m \angle BCD = m \angle 2. Solve the problem: Sum 4y 2y+18 90 Get 4y. | |
prob_53 | Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: CD = 5x+13, AB = 12x-8, l \widehat AB = l \widehat CD. Solve the problem: Equal 5x+13 12x-8 Get x. | |
prob_54 | Find m \angle QRT. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: RA \perp QT on T, CR \perp SQ on S, QS = QT = 8, m \angle SQR = 43. Solve the problem: Sum 43 V0 90 Equal V0 V1 Get V1. | |
prob_56 | Find the measure of \angle 3 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle BDC = 106, m \angle CBA = m \angle 3, m \angle CBD = m \angle 4, m \angle BCA = m \angle 1, m \angle BCD = m \angle 2. Solve the problem: Iso_Tri_Ang 106 V0 Equal V0 V1 Get V1. | |
prob_57 | Find m \angle C. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle EBC = 4x+17, m \angle EAD = 5x-1, m \angle ECB = 3y-20, m \angle EDA = 2y+1. Solve the problem: Equal 3y-20 2y+1 Get 3y-20. | |
prob_58 | Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AT \perp WS on T, WT = 4x-4, ST = 2x+2, RW = RS. Solve the problem: Equal 4x-4 2x+2 Get x. | |
prob_61 | A square is inscribed in a circle. What is the area of the circle? Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: DA = 5. Solve the problem: RNgon_B_Area 4 5 V0 RNgon_L_Area 4 V1 V0 Circle_R_Area V1 V2 Get V2. | |
prob_62 | Find the value of variable b. Lines that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle GFE = a, m \angle AFE = b, m \angle BFA = c, m \widehat GF = 56, m \widehat GD = e, m \widehat AF = d, m \widehat AD = 120. Solve the problem: Multiple b 2 120 Get b. | |
prob_63 | What is the length of LK? Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: LK = x+3.2, JL = 5x-0.2, JK = LK = 4x-1.3. Solve the problem: Equal x+3.2 4x-1.3 Get x+3.2. | |
prob_64 | Find m \angle M. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: NM = 11, m \angle PNM = 120, m \angle PMN = m \angle MPN. Solve the problem: Iso_Tri_Ang 120 V0 Get V0. | |
prob_65 | Find the measure of \widehat GH. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle HAG = 28. Solve the problem: Multiple 28 2 V0 Get V0. | |
prob_66 | Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AB = 4, EC = y, AC = 8, DB = 16, AF = x. Solve the problem: Sum 4 16 V0 Geo_Mean 4 V0 x Sum 8 y V1 Geo_Mean 8 V1 x Get y. | |
prob_67 | Find the area of the shaded region. Assume that the polygon is regular. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: BA = 7. Solve the problem: RNgon_H_Area 4 7 V0 Circle_R_Area 7 V1 Sum V1 V2 V0 Get V2. | |
prob_68 | Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AC \perp EB on B, AC = 23, CD = 16, m \angle EAB = 60. Solve the problem: Equal 16 V0 Gsin V1 V0 60 Para_Area 23 V1 V2 Get V2. | |
prob_69 | CDFG is a rhombus. Find m \angle GDF if m \angle GCD = b+3 and m \angle CDF = 6b-40. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: CG = 5a, FG = 3a+17. Solve the problem: Sum b+3 6b-40 180 Multiple V0 2 6b-40 Get V0. | |
prob_70 | Find the perimeter of the regular polygon figure. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: DE = 8. Solve the problem: Multiple 8 6 V0 Get V0. | |
prob_71 | Solve for c. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AB \parallel DE, m \angle DEC = c, m \angle DCE = d, m \angle CDE = b, m \angle CBA = 40, m \widehat DA = a. Solve the problem: Equal c 40 Get c. | |
prob_73 | Find the measure of \angle PQR. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: PQ = 9.6, PR = 5.9, RQ = 10.5. Solve the problem: Cos_Law 5.9 9.6 10.5 V0 Get V0. | |
prob_74 | \triangle ABC \sim \triangle DEF. BG is a median of \triangle ABC, and EH is a median of \triangle DEF. Find EH if BC = 30, BG = 15, and EF = 15. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: . Solve the problem: Proportion 30 15 15 V0 Get V0. | |
prob_75 | m \angle 4 = 101. Find the measure of \angle 7. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: BH \parallel AG, m \angle AEF = m \angle 8, m \angle FEG = m \angle 7, m \angle GED = m \angle 6, m \angle BDC = m \angle 1, m \angle CDH = m \angle 2, m \angle AED = m \angle 5, m \angle EDH = m \angle 3, m \angle BDE = m \angle 4. Solve the problem: Sum 101 V0 180 Get V0. | |
prob_76 | Use rhombus ABCD with AY = 6, DY = 3r+3, and BY = \frac{10r-4}{2}. Find m \angle ABD. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: . Solve the problem: Equal 3r+3 \frac{10r-4}{2} Gtan 6 \frac{10r-4}{2} V0 Get V0. | |
prob_77 | Find the perimeter of \triangle ABC if \triangle ABC \sim \triangle DBE, AB = 17.5, BC = 15, BE = 6, and DE = 5. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: BE = 6, ED = 5, AB = 17.5, BC = 15. Solve the problem: Proportion 6 15 5 V0 Sum 17.5 15 V0 V1 Get V1. | |
prob_78 | BD bisects \angle ABC, m \angle ABD = 6x+3, and m \angle DBC = 8x-7. Find m \angle ABC. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: . Solve the problem: Equal 6x+3 8x-7 Sum 6x+3 8x-7 V0 Get V0. | |
prob_79 | What is m \widehat XV? Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle VXZ = 40, m major \widehat XZ = 180. Solve the problem: Multiple 40 2 V0 Sum V0 180 V1 360 Get V1. | |
prob_80 | The angle bisectors of \triangle AEC meet at point G. Solve for the measure of \angle JGC. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: EC \perp HG on H, FC \perp EA on F, AC \perp GJ on J, CG = 26, GJ = 10. Solve the problem: Gcos 10 26 V0 Get V0. | |
prob_81 | What is the measure of \angle 3? Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: line l \parallel line m, line p \parallel line q, m \angle EDK = 105, m \angle KHI = m \angle 2, m \angle HKJ = m \angle 5, m \angle LKD = m \angle 3, m \angle KHE = m \angle 8, m \angle GHE = m \angle 1, m \angle DEH = m \angle 4, m \angle DEA = m \angle 6, m \angle CDB = m \angle 7. Solve t... | |
prob_82 | Find the measure of \angle 1 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle BDC = 106, m \angle CBA = m \angle 3, m \angle CBD = m \angle 4, m \angle BCA = m \angle 1, m \angle BCD = m \angle 2. Solve the problem: Iso_Tri_Ang 106 V0 Equal V0 V1 Get V1. | |
prob_83 | Quadrilateral EFGH is a rectangle. Find m \angle EFG. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: HG \perp EH on H. Solve the problem: Equal V0 90 Get V0. | |
prob_84 | For what value of variable x must ABCD be a parallelogram? Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AB = 2y+2, BC = y+4, CD = 3y-9, AD = 3x+6. Solve the problem: Equal 2y+2 3y-9 Equal y+4 3x+6 Get x. | |
prob_85 | GHJK is a square with diagonals intersecting at L. Given that GH = 2 and GL = \sqrt{2}, determine HK. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: HG = 2, GL = \sqrt{2}. Solve the problem: Multiple \sqrt{2} 2 V0 Get V0. | |
prob_86 | Find the perimeter of \triangle DBE if \triangle ABC \sim \triangle DBE, AB = 17.5, BC = 15, BE = 6, and DE = 5. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: BE = 6, ED = 5, AB = 17.5, BC = 15. Solve the problem: Proportion 17.5 V0 15 6 Sum V0 6 5 V1 Get V1. | |
prob_89 | If RL = 5, RT = 9, and WS = 6, find RW. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: LW \parallel TS. Solve the problem: Sum 5 V0 9 Proportion 5 V0 V1 6 Get V1. | |
prob_90 | Find XW. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: WY \perp BA on Z, XY = 12, ZY = WZ. Solve the problem: Equal 12 V0 Get V0. | |
prob_91 | Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AB = 3x-2, DA = 6y-8, DC = 2x+6, CB = 4y+6. Solve the problem: Equal 3x-2 2x+6 Get x. | |
prob_93 | Find m \widehat RMN. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle LCR = 3x+5, m \angle MCR = x-1, m \angle MCN = 60. Solve the problem: Sum 3x+5 x-1 180 Sum x-1 60 V0 Get V0. | |
prob_94 | If FGHJ is a kite, find m \angle GFJ. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: GH = FG, HJ = FJ, m \angle HGF = 128, m \angle HJF = 72. Solve the problem: Sum V0 V0 128 72 360 Get V0. | |
prob_95 | m \angle 1 = 94. Find the measure of \angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: FG \parallel DB, m \angle CEG = m \angle 6, m \angle ECD = m \angle 2, m \angle ACB = m \angle 8, m \angle CEF = m \angle 3, m \angle ECB = m \angle 7, m \angle HEF = m \angle 4, m \angle HEG = m \angle 5, m \angle ACD = m \angle 1. Solve the problem: Sum 94 V0 180 Get V0. | |
prob_96 | Rhombus ABCD is circumscribed about \odot P and has a perimeter of 32. Find HC. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AF = 3, DH = x. Solve the problem: Equal 3 V0 Get V0. | |
prob_97 | KN and JL are diameters. Solve for m \widehat MN. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle NQM = 55, m \angle KQL = 60. Solve the problem: Equal 55 V0 Get V0. | |
prob_98 | Find m \angle AEC. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle DEC = 65, m \angle AED = 80. Solve the problem: Sum 65 80 V0 Get V0. | |
prob_99 | Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: FD = 7, AE = AB = BC = DC = ED. Solve the problem: Circle_R_Area 7 V0 RNgon_L_Area 5 7 V1 Sum V1 V2 V0 Get V2. | |
prob_100 | If AC is parallel to BD and m \angle 1 + m \angle 3 = 90, what is the measure of \angle 2? Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AB = DC, m \angle ABG = m \angle 2, m \angle ABE = m \angle 1, m \angle ACE = m \angle 3. Solve the problem: Equal V0 90 Sum V0 V1 180 Get V1. | |
prob_101 | Triangles ABD and ADE are inscribed in \odot F with AB = BD. Find the measure of \angle 4 if m \angle 1 = 12x-8 and m \angle 2 = 3x+8. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle BAF = m \angle 3, m \angle EAF = m \angle 1, m \angle BDF = m \angle 4, m \angle FDE = m \angle 2. Solve the problem: Iso_Tri_Ang 90 V0 Get V0. | |
prob_102 | Find the measurement of EG. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: FG = 1.3, EF = 2.4. Solve the problem: Sum 1.3 2.4 V0 Get V0. | |
prob_103 | Solve for y. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: BD \perp BA on B, AD \perp BC on C, BA = z, AC = 2, BC = x, DC = 10, DB = y. Solve the problem: Sum 2 10 V0 Geo_Mean 10 V0 y Get y. | |
prob_104 | Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AE \perp DB on C, DA = EB = AB, m \angle ABC = x, m \angle ADC = 60, m \angle BEC = y. Solve the problem: Equal x 60 Get x. | |
prob_105 | Find m \widehat AC. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AB = 3x+2, BC = 5x-7, m \widehat AB = m \widehat BC = 109. Solve the problem: Sum V0 109 109 360 Get V0. | |
prob_106 | Find the value of m. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: CB \perp AD on D, CA \perp AB on A, AD = 5, CD = 7, BC = m. Solve the problem: Geo_Mean 7 V0 5 Sum 7 V0 m Get m. | |
prob_107 | m \widehat AB = 176, and m \widehat BC = 42. Solve for the measure of \angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle ABC = m \angle 2, m \angle BAC = m \angle 1, m \angle ACB = m \angle 3. Solve the problem: Sum 176 42 V0 360 Multiple V1 2 V0 Get V1. | |
prob_108 | Find m \angle G. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: GH = 10, FG = 8, HF = g, m \angle HFG = 40. Solve the problem: Sin_Law 40 10 V0 8 Sum V1 V0 40 180 Get V1. | |
prob_109 | Find x. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: AC \perp CB on C, AB = x, CB = 6\sqrt{2}, m \angle CAB = 45. Solve the problem: Gsin 6\sqrt{2} x 45 Get x. | |
prob_110 | Use rhombus QRST. Find m \angle QTP if m \angle RST = 56. Please first convert the diagram to sematic sequences. Then, solve the problem. | This is sematic sequences: m \angle PRQ = m \angle 1, m \angle PRS = m \angle 2, m \angle QPR = m \angle 3. Solve the problem: Iso_Tri_Ang 56 V0 Equal V0 V1 Get V1. |
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