BALTIC-WAY 1998 Problem 13

In a convex pentagon $A B C D E$, the sides $A E$ and $B C$ are parallel and $\angle A D E=\angle B D C$. The diagonals $A C$ and $B E$ intersect at $P$. Prove that $\angle E A D=\angle B D P$ and $\angle C B D=\angle A D P$.