It's 10 sided polygon. If the exterior is one fourth the size of the interior angle then the interior angle would be 4x and the exterior angle would be 1x. The sum of these angles are 180 which would make x equal to 36. Since the exterior angles always sum to 360, it doesn't take much to understand that 360 divided by 36 is 10 and that means there are 10 exterior angles making it have 10 sides.