I was just thinking of how the professor was talking about the angle 180 and 360 and thought of another proof which I think may work. Can someone verify it?
@angeliccanary That would definitely work! You found that the three angles, 180-a, 180-b, and 180-y must add to 360 degrees because they form a "full rotation." Actually, some people go the opposite way: they start with the fact that the angles in a triangle add to 180 degrees, and use that to actually prove that the exterior angles must add to 360 degrees... can you see how?