images
images listlengths 1
1
| problem
stringlengths 52
417
| answer
stringclasses 794
values | proID
stringlengths 1
4
|
|---|---|---|---|
<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
|
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 6