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!).