Question 13
Let $ABCD$ be a quadrangle, $|AD| = |BC|$, $\angle A + \angle B = 120^{\circ}$ and let $P$ be a point exterior to the quadrangle such that $P$ and $A$ lie at opposite sides of the line $DC$ and the triangle $DPC$ is equilateral. Prove that the triangle $APB$ is also equilateral.