平行线中常见拐角问题Word下载.docx
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B.45°
C.60°
D.90°
5.如图,直线l1∥l2,∠1=50°
,∠2=22°
,则∠3的度数为( )
A.28°
B.38°
C.68°
D.82°
6.如图,直线a∥b,∠1=50°
,2=30°
A.20°
B.30°
C.40°
D.50°
7.如图,AB∥CD,且∠A=25°
,∠C=45°
,则∠E的度数是( )
A.60°
B.70°
C.110°
D.80°
8.如图所示,AB∥DE,∠1=130°
,∠2=36°
,则∠3等于( )
A.50°
B.86°
C.94°
D.166°
9.已知,如图,AB∥CD,∠DCF=100°
,则∠AEF的度数为( )
B.110°
C.100°
10.如图,AD∥CB,∠D=43°
,∠B=25°
,则∠DEB的度数为( )
A.72°
B.68°
C.63°
D.18°
11.如图,AB∥DE,∠B+∠C+∠D=( )
B.360°
C.540°
D.270°
12.如图AB∥CD,∠ABE=120°
,∠ECD=25°
,则∠E=( )
A.75°
B.80°
C.85°
D.95°
13.如图,AB∥EF,BC⊥CD于C,∠ABC=30°
,∠DEF=45°
,则∠CDE等于( )
A.105°
B.75°
C.135°
D.115°
14.如图,AB∥CD,且∠BAP=60°
﹣α,∠APC=45°
+α,∠PCD=30°
﹣α,则α=( )
A.10°
B.15°
C.20°
D.30°
15.如图,AB∥CD,用含α,β,γ的式子表示θ,则θ=( )
A.α+γ﹣βB.β+γ﹣αC.180°
+γ﹣α﹣βD.180°
+α+β﹣γ
16.如图,AB∥MP∥CD,MN平分∠AMD,∠A=40°
,∠D=60°
,那么∠NMP的度数是( )
A.40°
D.10°
17.如图所示,AB∥CD,∠2=∠1,∠4=100°
,则∠3=( )
A.100°
B.120°
D.160°
18.如图所示,AB∥CD,则∠A+∠E+∠F+∠C等于( )
D.720°
19.如图,AB∥EF∥CD,∠ABC=46°
,∠CEF=154°
,则∠BCE等于( )
A.23°
B.16°
D.26°
20.如图所示,OP∥QR∥ST,若∠2=110°
,∠3=120°
,则∠1的度数为( )
B.50°
21.如图,已知AB∥ED,则∠B+∠C+∠D的度数是( )
22.如图,已知△ABC中,AB∥EF,DE∥BC,则图中相等的同位角有( )
A.二组B.三组C.四组D.五组
23.如图,∠ABE=110°
,若CD∥BE,则∠1度数为( )
B.60°
C.70°
24.如图,在△ABC中,∠C=90°
,若BD∥AE,∠DBC=20°
,则∠CAE的度数是( )
25.在△ABC中,∠ABC=90°
,∠A=50°
,BD∥AC,则∠CBD等于( )
C.45°
D.60°
26.如图,AB∥CD,∠ABF=∠ABE,∠CDF=∠CDE,则∠E:
∠F=( )
A.2:
1B.3:
1C.3:
2D.4:
3
27.如图所示,若AB∥CD,则∠A,∠D,∠E之间的度数关系是( )
A.∠A+∠E+∠D=180°
B.∠A﹣∠E+∠D=180°
C.∠A+∠E﹣∠D=180°
D.∠A+∠E+∠D=270°
28.(经典题)如图所示,两平面镜α、β的夹角为60°
,入射光线AO平行于β入射到α上,经两次反射后的反射光线O′B平行于α,则∠1的度数为( )
C.30°
D.75°
29.如图,已知AB∥DC,AD∥BC,∠B=80°
,∠EDA=40°
,则∠CDO=( )
A.80°
D.40°
30.如图,已知∠AOP=∠BOP,PC∥OA,PD⊥OA,若∠OPD=75°
,则∠BCP等于( )
A.15°
C.35°
31.如图,已知AB∥DE,∠B=20°
,∠D=130°
,那么∠BCD等于( )
C.80°
32.如图AB∥CD,∠1=140°
,∠2=90°
,则∠3的度数是( )
C.50°
33.如图,某市二环路修到长虹家电城区时,需拐弯绕城区而过.如果第一次拐的角A是130°
,第二次拐的角B是150°
,而第三次拐的角是C,这时的道路恰好和第一次拐弯之前的道路平行,则∠C等于( )
A.130°
B.140°
C.150°
34.如图,DE∥BC,∠D=2∠DBC,∠1=∠2,则∠DEB的度数为( )
D.无法计算
35.如图,已知AB∥DE,∠A=136°
,∠C=164°
,则∠D的度数为( )
D.120°
36.如图,AB∥CD,若EM平分∠BEF,FM平分∠EFD,EN平分∠AEF,则与∠BEM互余的角有( )
A.6个B.5个C.4个D.3个
37.如图,AB∥CD,FG⊥CD于N,∠EMB=α,则∠EFG等于( )
﹣αB.90°
+αC.180°
+αD.270°
﹣α
38.如图所示,b∥c,EO⊥b于点D,OB交直线C于点B,∠1=130°
,则∠2等于( )
39.如图,如果AB∥CD,CD∥EF,那么∠BCE等于( )
A.∠1+∠2B.∠2﹣∠1C.180°
﹣∠2+∠1D.180°
﹣∠1+∠2
40.如图,直线a∥b,Rt△BCD如图放置,∠DCB=90°
.若∠1+∠B=70°
,则∠2的度数为( )
B.40°
D.25°
41.已知,如图,AB∥CD,∠A=70°
,∠B=40°
,则∠ACD=( )
A.55°
D.110°
42.如图,∠1=50°
,如果AB∥DE,那么∠D=( )
C.130°
D.140°
43.如图,已知AB∥CD,BC平分∠ABE,∠C=33°
,则∠BED的度数是( )
A.16°
B.33°
C.49°
D.66°
44.如图所示,直线a∥b,∠B=16°
,∠C=50°
,则∠A的度数为( )
A.24°
B.26°
C.34°
D.36°
45.如图,AB∥EF,BC∥DE,∠B=70°
,则∠E的度数为( )
A.90°
46.如图,已知AB∥CD,∠C=70°
,∠F=30°
B.35°
D.45°
47.已知:
如图,AB∥CD∥EF,∠ABC=50°
,∠CEF=150°
,则∠BCE的值为( )
48.如图,直线a∥b,则∠ABD的度数是( )
A.38°
B.48°
C.42°
D.100°
49.如图,已知AB∥CD,∠DAB=60°
,∠B=80°
,AC是∠DAB的平分线,那么∠ACE的度数为( )
50.如图,直线a∥b,射线DC与直线a相交于点C,过点D作DE⊥b于点E,已知∠1=25°
A.115°
B.125°
C.155°
D.165°
51.如图,直线a∥b,直角三角形如图放置,∠DCB=90°
52.如图,AB∥ED,AG平分∠BAC,∠ECF=70°
,则∠FAG的度数是( )
A.155°
B.145°
D.35°
53.将一直角三角板与两边平行的纸条如图放置.已知∠1=30°
54.如图,∠1=40°
,如果CD∥BE,那么∠B的度数为( )
A.160°
55.如图,将三角形的直角顶点放在直尺的一边上,若∠1=65°
56.如图,已知AB∥CD,∠2=120°
,则∠1的度数是( )
C.120°
57.如图,桌面上有木条b、c固定,木条a在桌面上绕点O旋转n°
(0<n<90)后与b平行,则n=( )
A.20B.30C.70D.80
58.如图所示,已知AB∥CD,CE平分∠ACD,当∠A=120°
时,∠ECD的度数是( )
A.45°
59.如图,直线m∥n,则∠α为( )
A.70°
B.65°
60.如图,AB∥CD,∠BAC=120°
,则∠C的度数是( )
参考答案与试题解析
1.
【解答】解:
∵AB∥CD,
∴∠BAC+∠ACD=180°
,
同理∠DCE+∠CEF=180°
∴∠BAC+∠ACE+∠CEF=360°
;
又∵EH⊥CD于H,
∴∠HEF=90°
∴∠BAC+∠ACE+∠CEH=∠BAC+∠ACE+∠CEF﹣∠HEF=360°
﹣90°
=270°
.
故选:
B.
2.
如图,作EF∥AB,
∴EF∥CD,
∵EF∥AB,
∴∠α+∠AEF=180°
∵EF∥CD,
∴∠γ=∠DEF,
而∠AEF+∠DEF=∠β,
∴∠α+∠β=180°
+∠γ,
即∠α+∠β﹣∠γ=180°
D.
3.
作BD∥AE,如图,
∵AE∥C