Question

在△ABC中,AB=AC,点D在AB边上,且BD=BC=AD,则∠A的度数为多少?

Answer 1

∵AD＝BD

∴∠A＝∠ABD

∵∠BDC＝∠A＋∠ABD

∴∠BDC＝2∠A

∵BD＝BC

∴∠C＝∠BDC＝2∠A

∵AB＝AC

∴∠ABC＝∠C＝2∠A

∵∠A＋∠ABC＋∠C＝180°

∴∠A＋∠2∠A＋2∠A＝180°

∴5∠A＝180°

∴∠A＝36°