Question

Each exterior angle of a regular polygon is 45°. What is the sum of the interior angles of the polygon?

Answer 1

The sum of the interior angles of the polygon is `1080^o`

Explanation:

Sum of exterior angle of any polygon is `360^o`.

As each exterior angle is `45^o`, number of angles or sides of the polygon is `360^o/45^o=8`.

Further as each exterior angle is `45^o`, each interior angle is `180^o-45^o=135^o`.

As there are `8` interior angles each `135^o`

the sum of the interior angles of the polygon is `135^o xx8=1080^o`