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

1 Answer
Sep 21, 2016

Answer:

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#