Write for the incentre (it is the point where and all meet, of course). Write for the angles of the triangle, at respectively. Now mark on a diagram all the angles you can find that are equal to or . For example, the angles are all equal to . Also, , and so . Deduce that the lines and are perpendicular.

It follows that bisects , and therefore the triangle is isosceles. Hence the angle is equal to . Show by similar arguments that the angle is equal to , and conclude that the angle is .