Question

如图,三角形ABC中,外角∠ACD的平分线与∠ABC的平分线交于A1,∠A1BC与∠A1CD?

Answer 1

以A和A1两个角为例,∠ACD=∠A+∠ABC ,∠A1CD=1/2*∠ACD=1/2*∠A+1/2*∠ABC

=1/2*∠A+∠A1BC ,∠A1CD为外角=∠A1+∠A1BC

所以,∠A1=1/2∠A,因此,每分一次,角度变为一半

∠A4=1/2^4*∠A=1/16*∠A=4°