Question

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

Answer 1

In the figure above we have an irregular octagon `ABCDEFGH`.

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 `180^@`, the sum of 8 interior angles of octagon will be `6xx180^@=1080^@`

Extension

Comparing with this situation we can say that a polygon of n-sides can be divided into `n-2` triangles and thereby the sum of the interior angles of polygon of n-sides will be

`=(n-2)xx180^@`

Exercise

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