images images listlengths 1 1 | problem stringlengths 52 417 | answer stringclasses 794 values | proID stringlengths 1 4 |
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<image>As shown in the diagram, triangle RST is congruent to triangle XYZ, TR=x+21, ZX=2*x-14, ∠TRS=4*y-10°, ∠ZXY=3*y+5°. Find the value of y. | 15 | 1 | |
<image>As shown in the diagram, MN=3*x-4, NQ=15, PN=2*y+5, PQ=12, RM=18, RP=20, RQ=3*z-3, ∠MRQ=38°, ∠NQP=83°, ∠QNM=33°, MN and RP are opposite sides of the ▱ MRPN. Find the value of y. | 13/2 | 2 | |
<image>As shown in the diagram, BT=SB, QA=RA, QT=86, RS=54, the midsegment of quadrilateral AQTB is JK. Find JK. | 78 | 3 | |
<image>As shown in the diagram, WZ=23, XY=23, ∠ZWX=112°, XW is parallel to YZ, XYZW is a trapezoid. Find the measure of ∠YZW. | 68 | 4 | |
<image>As shown in the diagram, AC=20, CM=12, MB=30, CM is perpendicular to AM. Find the perimeter of triangle AMB. | 80 | 6 | |
<image>As shown in the diagram, AB=4/7, AC=x, BC=5/7, BA⊥CA. Find the value of x. | 3/7 | 8 | |
<image>As shown in the diagram, JK=10, MN=16, ∠KMN=98°, K is the center of ⊙K, MP is perpendicular to KP. Find the length of line LN. | 4*sqrt(5) | 9 | |
<image>As shown in the diagram, ∠FCD=x°, arc EDB=10*x°, arc EFD=40°, E is the center of ⊙E, CD is the tangent to circle E. Find the value of x. | 5 | 10 | |
<image>As shown in the diagram, ∠CFK=28°, ∠GKF=35°, ∠KAC=25°, ∠KHC=51°, EG is perpendicular to FG, HC is perpendicular to KC, KF is perpendicular to EF. Find ∠FEK. | 55 | 11 | |
<image>As shown in the diagram, AB=30, CD=30, ∠XCZ=40°, X is the center of circle X, AM⊥YM, DN is perpendicular to ZN. Find the measure of arc XBA. | 80 | 12 | |
<image>As shown in the diagram, AJ=2*x+3, CJ=8*y-36, JB=5*x, JD=4*y, AD and CB are opposite sides of the parallelogram ACBD. Find the value of y. | 9 | 14 | |
<image>As shown in the diagram, IB=1/2*x-7, JI=1/4*x+5, LD=66-2/3*y, NL=1/3*y-6, NL=LD, CJ is perpendicular to NJ, IB⊥DB, JI⊥LI. Find the value of x. | 48 | 15 | |
<image>As shown in the diagram, AB=10, AC=y, BC=x, ∠ABC=60°, BC is perpendicular to AC. Find the value of y. | 5*sqrt(3) | 16 | |
<image>As shown in the diagram, AB=8, AD=27, AE=12, CD is parallel to BE. Find BC. | 10 | 17 | |
<image>As shown in the diagram, AB=4*x-17, CD=2*x-1, ∠BCD=4*y-19°, ∠CBA=3*y+3°, ACDB is a parallelogram. Find the value of y. | 22 | 19 | |
<image>As shown in the diagram, AE=BE, BA=8, BC=8, BE=CE, DA=10, DC=10, ∠ADE=x°, DE is perpendicular to AE. Find sin(x). | 2*sqrt(2)/5 | 20 | |
<image>As shown in the diagram, ∠ABX=5*y-6°, ∠BXC=2*x+24°, ∠CAB=3*x-17°, ∠XCA=y+58°, quadrilateral ABXC is a ▱. Find the value of y. | 16 | 21 | |
<image>As shown in the diagram, ∠NJK=101°, JA∥NF. Find ∠HNJ. | 79 | 22 | |
<image>As shown in the diagram, SR=3*x-5, TR=2*x+7, TS=22, ∠RST=∠STR. Find RS. | 31 | 23 | |
<image>As shown in the diagram, YX=24, YZ=28, ∠XWZ=105°, WZYX is a parallelogram. Find ∠WZY. | 75 | 24 | |
<image>As shown in the diagram, AB=x, AD=3*sqrt(3), BD=9, CD=y, ∠ABC=30°, ∠BCA=60°, AD is perpendicular to CD, CA is perpendicular to BA. Find the value of x. | 6*sqrt(3) | 25 | |
<image>As shown in the diagram, AB=y, AC=x, BC=18, ∠ABC=30°, CA is perpendicular to BA. Find the value of y. | 9*sqrt(3) | 26 | |
<image>As shown in the diagram, ∠CHE=9*x-11°, ∠GDF=8*x+4°, BD∥EH. Find the value of x. | 15 | 28 | |
<image>As shown in the diagram, RS=5, TR=6, TS=3, ∠SRT=x°. Find the value of x. | 180*acos(13/15)/pi | 29 | |
<image>As shown in the diagram, AB=2*x+3, BC=5*x, DA=DC, quadrilateral ADCB is a parallelogram. Find the value of x. | 1 | 33 | |
<image>As shown in the diagram, ∠ABD=130°, ∠CBA=x°, ∠DBC=95°. Find the value of x. | 135 | 36 | |
<image>As shown in the diagram, AB=y, AC=8, BC=x, ∠BAC=60°, AC is perpendicular to BC. Find the value of x. | 8*sqrt(3) | 38 | |
<image>As shown in the diagram, EJ=6, LK=7, ML=4, quadrilateral JMLK is a ▱, JE is perpendicular to LE. Find the perimeter of quadrilateral JMLK. | 22 | 39 | |
<image>As shown in the diagram, AB=8, AC=14, BC=8, BX=x, BX⊥CX. Find the value of x. | sqrt(15) | 40 | |
<image>As shown in the diagram, NM=4, ∠NLM=∠PLN, ∠PLN=25°, LM is perpendicular to NM, NP is perpendicular to LP. Find ∠MNP. | 130 | 41 | |
<image>As shown in the diagram, ML=w, MN=2*y+5, MR=4*x-2, QL=12, QN=3*x+2, QR=3*y, quadrilateral NMRQ is a ▱. Find the value of w. | 12 | 43 | |
<image>As shown in the diagram, BA=6, CA=x, CB=x, ∠BAC=45°, ∠CBA=45°, AC is perpendicular to BC. Find the value of x. | 3*sqrt(2) | 44 | |
<image>As shown in the diagram, ∠EYQ=3*y+1°, ∠MAQ=3*x+11°, ∠YQF=4*x-5°, EF is parallel to YQ, QA is parallel to YM, YQ∥MA. Find the value of y. | 40 | 48 | |
<image>As shown in the diagram, FE=6, FG=3, FH=4, HG=2, △DEF is similar to △GFH.. Find Perimeter(△DEF). | 27/2 | 50 | |
<image>As shown in the diagram, ∠LWX=3*a+40°, ∠WXE=2*a+25°, ∠XZK=5*b-26°, WL∥XE, XN is parallel to ZK. Find the value of a. | 23 | 51 | |
<image>As shown in the diagram, ∠AGC=40°, ∠DGF=53°, CB⊥GB, FG is perpendicular to CG, GF is perpendicular to DF. Find the measure of ∠FDG. | 37 | 52 | |
<image>As shown in the diagram, ∠FOE=45°, the center of ⊙O is O, CO is perpendicular to AO, EO⊥BO. Find the measure of arc OAE. | 270 | 53 | |
<image>As shown in the diagram, BC=8, BH=12, O is the center of circle O, quadrilateral DCBH is a rectangle. Find the area of DCBH minus the area of the sector ODH. | 96-8*pi | 54 | |
<image>As shown in the diagram, AB=10, AC=6, BC=x, AC is perpendicular to BC. Find the value of x. | 8 | 55 | |
<image>As shown in the diagram, AB=14, ∠ADB=30°, DP is perpendicular to AP, ADCB is a rhombus. Find CP. | 7 | 57 | |
<image>As shown in the diagram, ∠BCE=∠EBC, ∠DAG=136°, ∠DEA=47°, ∠EFB=63°, ∠FED=69°. Find ∠EBC. | 32 | 58 | |
<image>As shown in the diagram, ∠LWX=53°, WL is parallel to XE, XN is parallel to ZK. Find ∠XZK. | 53 | 59 | |
<image>As shown in the diagram, AC=x, AD=4, BC=y, BD=9, CD=z, AC⊥BC, BD is perpendicular to CD. Find the value of z. | 6 | 60 | |
<image>As shown in the diagram, AB=8, CA=10, CB=a, ∠BAC=60°. Find the value of a. | 2*sqrt(21) | 61 | |
<image>As shown in the diagram, ∠CFD=x+36°, ∠DEC=2*y°, ∠ECF=78°, ∠FDE=110°, CE∥FD. Find the value of y. | 35 | 63 | |
<image>As shown in the diagram, ∠AJH=x°, ∠HGB=2*x°, A is the center of ⊙A, GB is perpendicular to HB, JH is perpendicular to GH. Find the measure of ∠BHG. | 30 | 64 | |
<image>As shown in the diagram, ∠CBD=55°, ∠FBG=35°, the center of ⊙B is B. Find the measure of ⌒BCD. | 305 | 65 | |
<image>As shown in the diagram, BA=3*x-13, BC=2*x+5, ∠BCD=∠CDB, ∠BDA=∠DAB, ∠DBC=60°. Find the value of x. | 18 | 66 | |
<image>As shown in the diagram, QT=x, RQ=6, SQ=18, SR=14, ∠TRQ=∠SRT. Find the value of x. | 27/5 | 67 | |
<image>As shown in the diagram, AD=5, BC=32, CD=12, AC is perpendicular to BC, BD is perpendicular to CD, triangle ACB is similar to triangle CBD.. Find Perimeter(△ACB). | sqrt(1193)+45 | 68 | |
<image>As shown in the diagram, ∠DEF=25°, ∠GFD=65°, EG is perpendicular to DG. Find the measure of ∠FDG. | 25 | 69 | |
<image>As shown in the diagram, ∠TYZ=52°, ∠ZYX=38°, TY is perpendicular to XY, XW is perpendicular to TW, YX is perpendicular to WX, YZ is perpendicular to TZ. Find ∠WTZ. | 52 | 72 | |
<image>As shown in the diagram, AB=y, AC=12, AD=BD, ∠CAB=x°, DB⊥CB, ADBC is a square. Find the value of x. | 45 | 74 | |
<image>As shown in the diagram, AN=10, BC=30, CN=5, AC is perpendicular to NC. Find the area of triangle ABC. | 75*sqrt(3) | 75 | |
<image>As shown in the diagram, DE=6*x-12, FE=4*y, GD=6*y-42, GF=2*x+36, EDGF is a parallelogram. Find the value of y. | 21 | 78 | |
<image>As shown in the diagram, BA=5, BC=12, DB=10, EB=x, O is the center of ⊙O. Find the value of x. | 6 | 79 | |
<image>As shown in the diagram, BC=x, BQ=6, QC=8. Find the value of x. | 2 | 80 | |
<image>As shown in the diagram, ∠DEF=5*x°, ∠FDE=5*x°, ∠GFE=9*x+7°. Find ∠GFE. | 70 | 81 | |
<image>As shown in the diagram, JL=y+4/5, LC=2*y-11/5, MI=12-3*x, TM=10-2*x, TM=MI, JT∥LM, LM∥CI. Find the value of y. | 3 | 83 | |
<image>As shown in the diagram, AB=32, AD=DC, BC=2*x-3, EF=12, EH=HG, FG=x-5, ∠BCD=∠FGH, ∠DAB=∠HEF. Find the value of x. | 31/2 | 84 | |
<image>As shown in the diagram, ∠ABC=110°. Find the measure of ∠CBD. | 70 | 85 | |
<image>As shown in the diagram, ∠DGH=64°, BC∥DE, DF is parallel to GH. Find the measure of ∠JGD. | 116 | 89 | |
<image>As shown in the diagram, WX=a+12, WZ=4*a-15, XY=YZ, WY perpendicular bisects ZX. Find the length of line WX. | 21 | 91 | |
<image>As shown in the diagram, ∠DHB=38°, ∠FDA=52°, HB⊥DB. Find the measure of ∠HDF. | 128 | 93 | |
<image>As shown in the diagram, arc DBC=170°, the center of circle D is D. Find the measure of ∠CAB. | 85 | 94 | |
<image>As shown in the diagram, ∠PNO=56°, ∠BMN=70°, B is the center of ⊙B. Find the measure of ⌒BOP. | 112 | 95 | |
<image>As shown in the diagram, ∠ACB=3*y+36°, ∠BDA=9*y-12°, ∠CBD=12*x+72°, ∠DAC=25*x+20°, quadrilateral BDAC is a parallelogram. Find the value of x. | 4 | 96 | |
<image>As shown in the diagram, AD=11, BC=25, CA and CD are one pair of adjacent sides of the kite BACD. Find Area(BACD). | 275/2 | 97 | |
<image>As shown in the diagram, ∠CBD=55°, ∠FBG=35°, the center of ⊙B is B. Find the measure of arc BFA. | 270 | 98 | |
<image>As shown in the diagram, PQ=25*sqrt(3), RQ=25, PQ is perpendicular to RQ. Find ∠QRP. | 60 | 99 | |
<image>As shown in the diagram, AB=z, AN=x, AY=5, YB=14, YN=y, BA is perpendicular to YA, YN is perpendicular to AN. Find the value of y. | 25/14 | 100 | |
<image>As shown in the diagram, AB=c, CA=b, CB=a, ∠ABC=60°, ∠CAB=30°, b=18, BC is perpendicular to AC. Find the value of c. | 12*sqrt(3) | 103 | |
<image>As shown in the diagram, AB=x, AC=y, BC=6, ∠BAC=30°, AC⊥BC. Find the value of x. | 12 | 104 | |
<image>As shown in the diagram, AD=15, PF=6, the centroid of triangle ACE is P. Find the length of line PC. | 12 | 105 | |
<image>As shown in the diagram, Area(ABCD) is 846, the area of quadrilateral EFGH is 376, CB=x, FG=24, quadrilateral ABCD is similar to quadrilateral EFGH. Find The ratio of similar quadrilaterals ABCD and EFGH. | 3/2 | 106 | |
<image>As shown in the diagram, AB=15*x+9, AC=7*x, BC=11*x+5, Perimeter(△CBA) is 320. Find CB. | 107 | 107 | |
<image>As shown in the diagram, ∠PRQ=115°, R is the center of circle R, NR is perpendicular to PR. Find ⌒RMQ. | 65 | 108 | |
<image>As shown in the diagram, BO=15, BO=CA, CE=7, CO=13, CO=BA, OE⊥AE. Find the perimeter of quadrilateral OCAB. | 56 | 110 | |
<image>As shown in the diagram, RQ=5, VS=11, S bisects segment RT, V bisects segment QU, quadrilateral QUTR is a trapezoid. Find the length of line UT. | 17 | 112 | |
<image>As shown in the diagram, FK=3*x-1, JK=6*y-2, KG=4*y+3, KH=2*x+3, FJHG is a ▱. Find the value of x. | 4 | 113 | |
<image>As shown in the diagram, AC=5, BC=x, ∠ABC=60°, ∠CAB=30°. Find the value of x. | 5*sqrt(3)/3 | 114 | |
<image>As shown in the diagram, ∠FOE=118°, ∠LDA=104°, OD∥FI. Find ∠OFI. | 118 | 115 | |
<image>As shown in the diagram, ∠GOI=3*y+1°, ∠HBI=3*x+11°, ∠OIE=4*x-5°, GE is parallel to OI, IB is parallel to OH, OI∥HB. Find the value of x. | 16 | 116 | |
<image>As shown in the diagram, AC=5*sqrt(26), AD=25, CB=sqrt(26), CD=5, DB=1, ∠BCD=y°, ∠DCA=x°, AD⊥CD, BC⊥AC. Find the value of Cos(CAD). | 5*sqrt(26)/26 | 117 | |
<image>As shown in the diagram, the center of ⊙A is A, DF is the tangent to circle A. Find ∠AFD. | 90 | 118 | |
<image>As shown in the diagram, WX=9*x, WY=6*x+3, WY=YX, XW=WY, YX=4*x+5. Find the measure of ∠XWY. | 60 | 119 | |
<image>As shown in the diagram, CB=4*w-7, CD=11, ED=3*z+10, RS=2*w+13, RU=12, UT=z+16, ∠CBE=2*x+9°, ∠EDC=2*y-31°, ∠STU=y+11°, ∠URS=49°, quadrilateral BEDC is mirror congruent to quadrilateral RSTU. Find the value of x. | 20 | 122 | |
<image>As shown in the diagram, WT=3, WX⊥YX, XY is perpendicular to ZY, YZ⊥WZ, ZW⊥XW, XYZW is a square. Find the length of line XY. | 3*sqrt(2) | 124 | |
<image>As shown in the diagram, ∠ABH=3*p-10°, ∠CDB=6*r+5°, ∠JAB=4*p+15°, AJ is parallel to BH, CI∥AL. Find the value of r. | 10 | 125 | |
<image>As shown in the diagram, DA=3, DC=CB, DC⊥AC. Find the length of line AB. | 3 | 126 | |
<image>As shown in the diagram, ∠ADK=96°, ∠HGJ=42°, GA∥HD. Find ∠GHD. | 42 | 127 | |
<image>As shown in the diagram, ∠GKM=62°. Find the measure of ∠BKG. | 118 | 128 | |
<image>As shown in the diagram, SR=5, TR=3, TS=4, RT is perpendicular to ST. Find the value of Cos(TSR). | 4/5 | 129 | |
<image>As shown in the diagram, AJ=2*x+3, BJ=5*x, JC=8*y-36, JD=4*y, AD and CB are opposite sides of the parallelogram ACBD. Find the value of x. | 1 | 132 | |
<image>As shown in the diagram, AB=36, AD=22, ∠BCE=30°, BCDA is a parallelogram, CE is perpendicular to BE. Find the perimeter of quadrilateral BCDA. | 116 | 133 | |
<image>As shown in the diagram, CB=44, EA=19, ∠ACE=30°, BDAC is a parallelogram, DE⊥CE. Find Area(BDAC). | 836*sqrt(3) | 134 | |
<image>As shown in the diagram, AC=25, AD=21, EB=20, CADB is a ▱, DE is perpendicular to BE. Find the area of CADB. | 420 | 135 | |
<image>As shown in the diagram, AC=b, BA=c, BC=a, ∠ABC=60°, ∠CAB=30°, b=3, BC is perpendicular to AC. Find the value of c. | 2*sqrt(3) | 136 | |
<image>As shown in the diagram, JK=33, LK=x, ∠KLJ=45°, JK⊥LK. Find the value of x. | 33 | 139 | |
<image>As shown in the diagram, CB=6, ∠CAB=60°, quadrilateral ABCD is a rhombus. Find AC. | 6 | 143 |
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