# Polygon Interior Angles Sum Theorem

Polygon Interior Angles Sum Theorem

The sum of the measures of the interior angles of a convex polygon with $n$ sides is

$\left(n-2\right)180°$ .

Example :

Find the sum of the measures of the interior angles of an octagon.

Solution:

An octagon has $8$ sides. So, $n=8$ .

Substitute $8$ for $n$ in the formula.

The sum of the measures of the interior angles of an octagon $=\left(8-2\right)180°$ .

$\begin{array}{l}=6×180°\\ =1080°\end{array}$

The sum of the measures of the interior angles of an octagon is $1080°$ .