Question

如图,已知三角形ABC中,BM平分∠ABC,CM平分∠ACB的外角,求证∠A=2∠M

Answer 1

∠M+∠MBC+∠MCB=180

∠MBC=1/2∠ABC

∠MCA=1/2∠ACD

∠M+1/2∠ABC+1/2∠ACD+∠ACB=180

2∠M+∠ABC+∠ACD+2∠ACB=360

∠ACD+∠ACB=180

2∠M+∠ABC+∠ACB=180

∠A+∠ABC+∠ACB=180

所以∠A=2∠M