如图,在矩形ABCD中,AB=2BC,在CD上取一点E,使AE=AB,则∠EBC的度数为_.
题目
如图,在矩形ABCD中,AB=2BC,在CD上取一点E,使AE=AB,则∠EBC的度数为______.
![](http://hiphotos.baidu.com/zhidao/pic/item/241f95cad1c8a786ec82edba6409c93d71cf50dd.jpg)
答案
∵四边形ABCD是矩形,∴∠D=∠ABC=90°,AD=BC,DC∥AB,∵AB=AE,AB=2CB,∴AE=2AD,∴∠DEA=30°,∵DC∥AB,∴∠DEA=∠EAB=30°,∵AE=AB,∴∠ABE=∠AEB=12(180°-∠EAB)=75°,∵∠ABC=90°,∴∠EBC=90°-75...
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