Question

已知在三角形ABC中,AB=AC,将三角形ABC绕点B顺时针旋转到三角形A'BC'的位置,使点A在BC上,且A、A'、C

Answer 1

由旋转可得：∠ABC=∠CBC',AC=AC'

∵AB=AC,AB=A'B

∴∠BAA'=∠BA'A,A'B=A'C'

∴∠A'BC'=∠A'C'B

∵AB=AC,∴∠ABC=∠ACB

∴∠ABC=∠ACB=∠A'BC'=∠A'C'B

设∠ABC=X,则X+2X+2X=180

∴X=36°,即∠ABC=36°