Struggling through a geometry problem

My older son picked an interesting challenge problem from Mathcounts for our movie this morning. As with most Mathcounts problems there is a quick way to solve it, but he didn’t see that quick way.

It was interesting watching him work his way through it:


It was tricky for him to see how to proceed although he did have most of what he needed on the board. I asked him to look at some of the angle relationships and that helped him get to the end: