∠ ABP=1/2(∠ A+∠ ACB)∠ BPC=180-（∠PBC+1/2∠PCB)=180-(∠ABC+1/2(∠ A+∠ ACB)+1/2∠ACB)=180-(∠ABC+∠ABC+1/2∠A)=180-(180-∠A+1/2A)=1/2∠A=40°
