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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.**View the archive of all weekly problems grouped by curriculum topic*