如图,在△ABC中,∠C=90,DE是AB的垂直平分线,∠CAE=∠B+30°,求∠AEB的度数.
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如图,在△ABC中,∠C=90,DE是AB的垂直平分线,∠CAE=∠B+30°,求∠AEB的度数.
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106214350-54905.png) |
答案
已知DE垂直且平分AB⇒AE=BE⇒∠EAB=∠B 又因为∠CAE=∠B+30° 故∠CAE=∠B+30°=90°-2∠B⇒∠B=20° ∴∠AEB=180°-20°×2=140°. |
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