Angles in regular polygons.

A regular polygon is one where all of the sides are the same length, and all of the angles are the same size.

To find the size of an interior angle of a regular polygon my way, you need to know what an interior and exterior angle are of a polygon. You need to extend a line to get the exterior angle

My favorite trick uses exterior angles. For every polygon, the exterior angles add up to 360°. This is most obvious if you make the polygon really small so all you can see are the exterior angles:

So, to find the size of an exterior angle you just have to divide 360° by the number of angles. In this case the size of an exterior angle of a regular 15-gon is 360°/15=24°.

Now, the exterior ang interior angles lie on a line, so they add up to 180°. If you know the measure of the exterior angle, you can find the measure of the interior angle by subtracting from 180°. In this case, the measure of an interior angle of a regular 15-gon is 180° - 24° = 156°.