Explanation:
Here's one way:
Choose a point P interior to the polygon and draw a segment from that point to each vertex. These segments will divide an n-sided polygon into n triangles. These will have a total angle measure of ...
total interior angles of n triangles = 180°×n
The n angles having a vertex at point P have a sum of 360°. Subtracting this total from the total of all triangles gives the sum of interior angles around the perimeter of the polygon: 180°×n - 360° = 180°×(n -2).
