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2. 如图7-10,将三角板的直角顶点放在直尺的一边上,若$∠1= 65^{\circ }$,则$∠2$的度数为()
A. $10^{\circ }$
B. $15^{\circ }$
C. $20^{\circ }$
D. $25^{\circ }$
A. $10^{\circ }$
B. $15^{\circ }$
C. $20^{\circ }$
D. $25^{\circ }$
答案
D
3. 已知直线$a// b$,把一块含有$30^{\circ }$角的直角三角板如图7-11放置,$∠1= 30^{\circ }$,三角板的斜边所在直线交b于点A,则$∠2$的度数为()
A. $50^{\circ }$
B. $60^{\circ }$
C. $70^{\circ }$
D. $80^{\circ }$
A. $50^{\circ }$
B. $60^{\circ }$
C. $70^{\circ }$
D. $80^{\circ }$
答案
B
4. 将一个长方形纸片折叠成如图7-12所示的图形,若$∠ABC= 26^{\circ }$,则$∠ACD$的度数为()
A. $128^{\circ }$
B. $138^{\circ }$
C. $120^{\circ }$
D. $150^{\circ }$
A. $128^{\circ }$
B. $138^{\circ }$
C. $120^{\circ }$
D. $150^{\circ }$
答案
A
5. 如图7-13,$AB// CD$,AD平分$∠BAC$,$∠1= 30^{\circ }$,则$∠2$的度数为()
A. $15^{\circ }$
B. $30^{\circ }$
C. $45^{\circ }$
D. $60^{\circ }$
A. $15^{\circ }$
B. $30^{\circ }$
C. $45^{\circ }$
D. $60^{\circ }$
答案
B
6. 如图7-14,已知$AB// DE$,$∠ABC= 70^{\circ }$,$∠CDE= 140^{\circ }$,则$∠BCD$的度数为()
A. $20^{\circ }$
B. $30^{\circ }$
C. $40^{\circ }$
D. $70^{\circ }$
A. $20^{\circ }$
B. $30^{\circ }$
C. $40^{\circ }$
D. $70^{\circ }$
答案
B
1. 如图7-15,$AC// DF$,B,E分别是AC,DF上的点,连接BD,CE,若$∠1= 80^{\circ }$,$∠2= 100^{\circ }$,求证：$∠C= ∠D$。
答案
$\because \angle 1=80^{\circ},\angle 2=100^{\circ}$，
$\therefore \angle 1+\angle 2=180^{\circ}$. $\therefore BD// CE$.
$\therefore \angle D=\angle CEF$.
$\because AC// DF$，$\therefore \angle C=\angle CEF$.
$\therefore \angle C=\angle D$.
$\therefore \angle 1+\angle 2=180^{\circ}$. $\therefore BD// CE$.
$\therefore \angle D=\angle CEF$.
$\because AC// DF$，$\therefore \angle C=\angle CEF$.
$\therefore \angle C=\angle D$.
