Explain how the formula for finding the sum of the interior angle measures of a polygon is derived.

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).