Angles in Polygons
Shape 
Picture 
Number of Sides 
Interior Angle 
Sum of Interior Angles 
Exterior Angle 
Triangle 
3 
60 
180 
120 

Square 
4 
90 
360 
90 

Pentagon 
5 
108 
540 
72 

Hexagon 
6 
120 
720 
60 

Octagon 
8 
135 
1080 
45 

n agon 
To see why the angles in a triangle add tonotice that a triangle has three sides so n=1 and the angles add to 180, a square can be cut into two triangles, each with internal angles 180, so all the internal angles of both triangles sum to 360. Consider the pentagon below. It is cut into three triangle, each with internal angles that sum to 360, so the internal angles of a pentagon sum to 3*180 =540.