Calculate the number of sides of a regular polygon whose interior angles are each 156 degrees?

Answer 1

Exterior angle = 180-156 = 24 degrees

Number of sides = 360/24 = 15 sides.

If you can't remember the formula, then remember this to help figure it out:

The regular polygon can be divided into triangles (like Pizza slices). Each triangle is an isosceles triangle and all of them are congruent (since it's a regular polygon).

Take one of the triangles: each of the 'leg angles' will be half of the polygon angle (the leg of the triangle has bisected the polygon angle). So these two angles will add together to be the same measure as the polygon angle (call it Ap). So the other angle in the triangle is in the center and all these pizza slice angle make a circle in the middle (360°). Since the triangle sums to 180°, the angle in the middle is (180° - Ap), then you have:

Number of sides = (360°) / (180° - Ap), or in this case: 360/(180-156) = 15 sides.