If the exterior angle is 156 degrees, the opposite angle is 156 degrees. 156 + 156 = 312 degrees. A circle of 360 degrees - 312= 48, therefore the sum of the remaining 2 angles is 48. Divide these by 2 = 24. T find the number of sides, 360 divided by 24 = 15. Therefore a polygon with an exterior angle of 156 degrees has 15 sides. Stop cheating and start to learn ;-)