# The Polygon Angle Sum Proof

The video above shows why the formula for the sum of the interior angles of a polygon with n sides is equal to $180(n-2)$. The polygon angle sum theorem shows the relationship between the number of sides of a polygon and the sum of its interior angles. The expression $n - 2$ is the maximum number of triangles that can be formed in a polygon by drawing  non-overlapping diagonals. The video above was labeled as a conjecture because the assumption is that it has not been proven that $n - 2$ is indeed the number of triangles for all polygons with $n$ sides. If we make this assumption is true, then the conjecture in the video becomes a proof.