Polygon angle sum theorem and the distributive property

We did this in class today as a warmup activity. I've always led students toward the first example but we made kind of a cool connection to the distributive property when we tried to make a student's picture work when they drew the triangles from the center of the figure instead of from a vertex.

In the first example all angles in the triangle add to the total measure of the polygon.

In the second example, the interior angles for the triangles (center) do not make up any of the polygon interior angles so we subtract them. To make the connection rather than writing it as 360 I wrote it as 2•180.