Question 565065
Assuming that this is a regular polygon...
The easiest way to do this is to recall that the sum of the EXTERIOR angles is 360, and that an interior angle + its exterior angle = 180 (because they make a straight line).  Thus, if the interior angles are each 156, the exterior angles are each 180-156=24.  Now, if you take 360/24 (because each exterior angle is 24 and they need to add to 360), you get 15.  Thus, there are 15 sides.