# What is the sum of the measures of the interior angles of an octagon?

##### 1 Answer

In the figure above we have an irregular octagon

5 diagonals each originating from A are drawn.These diagonals divide the octagon into 6 triangles.

It is obvious from the figure that the sum of the measures of the interior angles of the octagon is equal to the sum of the interior angles of 6 triangles.

As we know that sum of the interior angles of a triangle is

**Extension**

Comparing with this situation we can say that a polygon of **n-sides** can be divided into

**Exercise**

How will you get the sum of 8 interior angles of a concave irregular octagon using following figure?