Prove that AP is the bisector of ∠BAC external angle by using the property theorem and judgment theorem of angular bisector! And ∠BAC=2∠BPC is provable! Based on the properties of ∠BPC = 40° and angle bisector,

∠ ACD-2 ∠ ABC = 2× 40 = 80, that is ∠ BAC = 80,

Then the exterior angle of ∠BAC is 100, and ∠ Cap = × 100 = 50.

I don't know the angle. APB