# 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

$\left(n-2\right)180\xb0$ .

**
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 $=\left(8-2\right)180\xb0$ .

$\begin{array}{l}=6\times 180\xb0\\ =1080\xb0\end{array}$

The sum of the measures of the interior angles of an octagon is $1080\xb0$ .