Simply divide the circumference of a circle by n. That gives us a length so that we may place n points on the circle, each the same distance from the 2 adjacent points.

Now joining each pair of neighboring points we get a shape which can be rotated (360/n) degrees without any apparent change. That is to say, all interior angles are equal and the shape has some symmetry, in that it can be rotated and will still appear the same.

You may know that all triangles have interior angles that sum to 180 degrees. Can you use this fact to calculate an interior angle of an n-gon?