如图,点E,B,C分别在DF,AD,EA上,且AB=AC,BD=BF,EA=ED,求∠BAC的度数.

题目

如图,点E,B,C分别在DF,AD,EA上,且AB=AC,BD=BF,EA=ED,求∠BAC的度数.
有图

答案

∵AB=AC
BD=BF
EA=ED
∴∠ABC=∠ACB
∠D=∠F
∠D=∠A
∵∠ABC=∠D+∠F=2∠D
∴∠ABC=2∠A
∵∠ABC+∠ACB+∠A=180°
∴2∠A+2∠A+∠A=180°
∠A=36°
即∠BAC=36°