Question

在△ABC中，延长BC到D，∠ABC的平分线与∠ACD的平分线相交于点E，∠EBC的平分线与∠ECD的平分线交于点F

在△ABC中，延长BC到D，∠ABC的平分线与∠ACD的平分线相交于点E，∠EBC的平分线与∠ECD的平分线交于点F，若∠A=86°，求∠F的度数

Answer 1

∵∠ACD=∠A+∠ABC
CE平分∠ACD
∴∠ACE=1/2∠ACD=1/2∠A+1/2∠ABC
∵BE平分∠ABC
∴∠CBE=1/2∠ABC
∴∠BCE=∠ACB+∠ACE=∠ACB+1/2∠A+1/2∠ABC
∴∠E=180°-∠CBE-∠BCE
=180°-1/2∠ABC-(∠ACB+1/2∠A+1/2∠ABC)
=180°-∠ABC-∠ACB-1/2∠A
=∠A-1/2∠A
=1/2∠A
=43°
同理∠F=1/2∠E=43°/2=21.5°