Sum of Internal Angles of Polygon

Theorem
The sum of all internal angles of a polygon with $n$ sides is given by the formula $S = 180^circ (n-2)$.

Proof
For convex polygons, name a vertex as $A_1$, go clockwise and name the vertices as $A_2$, $A_3$, ..., $A_n$.

By joining $A_1$ to every vertex except $A_2$ and $A_n$, one can form $(n-2)$ triangles.

The sum of internal angles of a triangle is $180^\circ$.

Therefore, the sum of internal angles of a polygon with $n$ sides is $180^\circ(n-2)$.