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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.

 

 

This problem is taken from the UKMT Mathematical Challenges.