Two exterior triangles

Weekly Problem 35 - 2009
Two equilateral triangles have been drawn on two adjacent sides of a square. What is the angle between the triangles?

Problem



A square is labelled clockwise $ABCD$. $P$ and $Q$ are points outside the square such that triangles $ABP$ and $BCQ$ are both equilateral.

How big is angle $PQB$?

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.