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Incentre Angle

Age 14 to 16 Short Challenge Level:

The three angle bisectors of triangle $LMN$ meet at a point $O$ as shown. 
 
$\angle LNM$ is $68^{\circ}$. What is the size of $\angle LOM$?
 
 
 
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.