How do we use a polygon's exterior angles?

Exterior Angle Sum Conjecture

For any polygon, the sum of the measure of a set of exterior angles is 360°.

Regular - Equilateral, Equiangular

Ex 1: 

What is the measure of an exterior angle of an equiangular pentagon? 

Solution:

Pentagon= 5 sides 

Sum of exterior angles= 360°

measure of each exterior angle= ?

So, 360 ÷ 5(# of sides)= 72°

Ex 2: 

How many sides does a regular polygon have if each exterior angle measures 24°?

Solution:

# of sides= ?

Sum of exterior angles= 360°

measure of each exterior angle= 24°

So, 360 ÷ 24 = 15, 15 sides 

http://www.geom.uiuc.edu/~dwiggins/conj09.html