The sum of the interior angles of the polygon will equal the number of triangles drawn, times 180 degrees. But it's not actually necessary to draw all of those triangles.

The sum of the interior angles of an n-sided polygon is given by the formula: S = (n – 2) × 180º. This is because every n-sided polygon can be cut into (n − 2) triangles, each with total internal ...

By definition, the interior angles of a regular polygon are all equal, and since we know the number of angles (n) and their sum (180(n − 2)), we can just divide to compute the measure of each ...

This is true for any polygon with n sides, regular or not, and it follows from the fact that an n-sided polygon can be divided into (n − 2) triangles, and the sum of the measures of the interior ...