Find the number of sides of a regular polygon whose interior angle is 156 degrees

Recall that the sum of the exterior angles is 360, and that an interior angle + an exterior angle = 180

Thus, if the interior angles are each 156, the exterior angles are each 180-156=24.

Now take 360/24 (because each exterior angle is 24 and they need to add to 360), you get 15. Thus, there are 15 sides.