The exterior and the interior angles add up to 180º. To find the exterior angle you subtract 108º from 180º.
180º-108º=72º
That's the angle of one exterior angle. The sum of all the exterior angles is 360 degrees. If you divide 360º by one exterior angle 72º you get the number of sides of the polygon.
360º/72º=5
This polygon is a pentagon as it has 5 sides.