Can you please explain College Board Test 5 Section 4 #36?

I understand that angle A is half of x- the only part of the college board explanation I’m not understanding is why we do (360-x) while setting up the equation. Thanks!

Sure. Without looking at CB’s solution, here’s how I do it.

First, as you pointed out, the measure of angle A is half of x°. That’ll be useful. The other thing I think is useful is to draw segment BC and mark the angles you create (I’ll say their measures are b° and c°). Now you’ve got two triangles, ABC and PBC.

Each triangle, of course, has angles that add up to 180°. You can write two equations that show this:

Triangle ABC:

Triangle PBC:

All you need to do to solve for x is set those left sides equal to each other since they both equal 180 (b and c will cancel right out!).