Polygon Interior Angles

The interior angles of a polygon are the angles at each vertex that are on the inside of the polygon. There is one per vertex. So for a polygon with N sides, there are N vertices and N interior angles.
Each angle A = 180(N - 2)/N degrees where N is the number of sides.
This means the sum of all the interior angles of a polygon is
180(N - 2)

Here's how that's computed: We'll use a pentagon as an example.
Start with a pentagon and locate its center:

Cut the pentagon into triangles by connecting the center to each vertex. This makes 5 triangles with a common vertex at the center. Since there are 5 of them, the center angle of each triangle is
360^o/5 = 72^o
That makes the sum of the other 2 angles of each triangle
180^o - 72^o = 108^o.
Each of the other angles of the triangle are 108/2 = 54^o
Looking at the image you can see that 2 of these angles makes a pentagon interior angle, so the interior angles of a pentagon are 108^o each.

Let's try this on a larger polygon, one with 20 sides!
So, all the triangles vertices meet at the center and there are 20 of them, so each triangle vertex angle = 360^o/20^o = 18^o
That makes the sum of the other 2 angles 180^o - 18^o = 162^o which is the size of the interior angle of a 20-sided figure which, by the way, is an icosagon.