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Two Exterior Triangles
Age 11 to 14
ShortChallenge Level 
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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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