Simplified:

A triangle from center of the n-gono to 2 near corners, will have in center 360/n degrees. Easy to understand as you actually divide a circle into n arcs.

Each triangle (n triangles total) will have the other 2 corners equal and equal to (180-(360/n))/2

Each angle of the n-gono between it;s sides will be consisted of the angles of 2 triangles, thsu it will be

2 X (180-(360/n))/2 = 180 - 360/n