Calculate the interior angles of polygons

A polygon is a plane figure formed by three or more line segments. The points where the sides meet are called vertices, and sum of the lengths of a polygon’s sides is its perimeter. If all of the sides and angles of a polygon are equal, it is called a regular polygon. In the diagram below, both shapes are hexagons, but the one on your left is a regular, while the one on the right is irregular.  Equal sides or angles are illustrated with daggers |.

The simplest of all polygons is a triangle. It has three sides and the total sum of its interior angles is 180°. In this section, you’ll learn how to calculate the sum of the interior angles of any polygon. The formula that’s used to calculated the total sum is:

Sum of Angles


Where represents the total sum and n represents the number of sides. Let’s take a look at four different examples in increasing difficulty.