如图,在△ABC中∠ABC的平分线与∠ACE的平分线交于D点,若∠A=80°,求∠D的度数

如图,在△ABC中∠ABC的平分线与∠ACE的平分线交于D点,若∠A=80°,求∠D的度数
如图,在△ABC中∠ABC的平分线与∠ACE的平分线交于D点,若∠A=80°,求∠D的度数

如图,在△ABC中∠ABC的平分线与∠ACE的平分线交于D点,若∠A=80°,求∠D的度数
∵BD平分∠ABC,CD平分∠ACE
∴∠DBC=1/2∠ABC
∠ACD=1/2∠ACE=1/2(180°-∠ACB)
∴∠D=180°-∠DBC-∠ACB-∠ACD
=180°-1/2∠ABC-∠ACB-1/2(180°-∠ACB)
=180°-1/2∠ABC-∠ACB-90°+1/2∠ACB
=90°-1/2∠ABC-1/2∠ACB
=90°-1/2(∠ABC+∠ACB)
=90°-1/2(180°-∠A)
=1/2∠A
=40°