如图BP,CP分别平分∠ABC和∠ACD若∠A=40°求∠P

∵∠ACD=∠A+∠ABC,CP平分∠ACD
∴∠PCD=∠ACD/2=（∠A+∠ABC）/2
∵BP平分∠ABC
∴∠PBC=∠ABC/2
∴∠PCD=∠P+∠PBC=∠P+∠ABC/2
∴∠P+∠ABC/2=（∠A+∠ABC）/2
∴∠P=∠A/2=40°/2=20°

∵BP、CP分别平分∠ABC和∠ACD
∴∠PBC=1/2∠ABC
∠ACP=∠DCP=1/2∠ACD=1/2（180°-∠ACB）
∵∠DCP=∠PBC+∠P
∴∠P=∠DCP-∠PBC
=1/2（180°-∠ACB）-1/2∠ABC
=1/2（180°-∠ACB-∠ABC）
=1/2∠A
=20°