In the diagram, $\angle MON = 130^{\circ}$. The reflection of $OP$ in $OM$ is $OQ$ and the reflection of $OP$ in $ON$ is $OR$.

What is the size of $\angle QOR$?

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.