Sum of Internal Angles of Polygon/Proof 1

Proof
The Polygon Triangulation Theorem shows that there exists a triangulation of the polygon that consists of $n - 2$ triangles.

The sides of these triangles are sides and chords of the polygon.

Hence the vertices of the triangles are vertices of the polygon.

Sum of Angles of Triangle equals Two Right Angles shows that the sum of the internal angles of a triangle is $180 \degrees$.

As the triangulation covers the polygon, the sum of the internal angles of the vertices of the triangles in the triangulation is equal to $S$.

So:


 * $S = \paren {n - 2} 180 \degrees$