How do the sides of a polygon relate to its interior angle's degrees?

This method I'm going to tell you only works on regular polygons (all sides are congruent)! It's a method which will tell you the degree of each interior angle of the polygon. Since regular polygons all have congruent sides, all angles will have the same degree. Does not work with irregular polygons!
It's a very simple method, you really just need to know how many angles/sides the polygon has. The equation is 180(n-2)/n. 
n= number of angles/sides the polygon has
Example:

This is a regular hexagon. A hexagon has 6 sides and 6 angles. Therefore we plug 6 as n.

180(6-2)/6

180(4)/6

720/6

120

Each of a regular hexagon's interior angles have a measurement of 120 degrees.

You will later notice (after trying out different regular polygon) that the more sides and angle a regular polygon has, the more degrees its interior angles will have. 

Example:

  Regular hexagons angle's measurement: 120 degrees

Regular pentagons angle's measurement: 108 degrees

 
Squares angle's measurement: 90 degrees

Equilateral triangles angle's measurement: 60 degrees