What is the interior angle and exterior angle of a 16-gon? show your work.

If we divide 360 by the number of sides, 16, we will get the measure of one of the 16 central angles.  360/16 = 22.5.  The vertex angle of one of the triangles that makes up this 16-gon is 22.5.  That means that each of the base angles measure 78.75.  If we put 2 of these triangles next to each other, 2 sides touching, the bases of both those triangles meet to form an interior angle.  Two base angles of 78.75 together form the interior angle: 78.75+78.75 = 157.5.  An interior angle measures 157.5.  The exterior angle then has to measure 180-157.5 which is 22.5, same as the vertex angle of 1 of the triangles that make up this 16-gon.