An
exterior angle of a polygon is
an angle that forms a linear pair with one of the angles of the
polygon.


Two
exterior angles can be formed at each vertex of a polygon.
The exterior angle is formed by one side of the polygon and
the extension of the adjacent side. For the hexagon
shown at the left, <1 and <2 are exterior angles for that
vertex. Be careful, as <3 is NOT an exterior angle.

Note: While it is
possible to draw TWO (equal) exterior angles at each
vertex of a polygon, the sum of the exterior angles
formula uses only ONE exterior angle at each vertex. 
Formula:
Sum exterior angles
of any
polygon = 360°
(using one exterior angle at a vertex) 


Finding
the sum of the exterior
angles of a polygon is
simple. No matter what type of polygon you have, the sum
of the exterior angles is
ALWAYS
equal to
360°.
If you are working with a
regular polygon, you can determine the size
of EACH exterior angle by simply dividing the sum, 360, by the number of
angles. Remember,
the formula below will ONLY work in a
regular
polygon.

Formula:
Each exterior angle (regular
polygon) =


1. 
Find
the sum of the exterior angles of:
a) 
a
pentagon 
Answer:
360^{0} 
b) 
a
decagon 
Answer:
360^{0} 
c) 
a
15 sided polygon 
Answer:
360^{0} 
d) 
a
7 sided polygon 
Answer:
360^{0} 

2. 
Find
the measure of each exterior angle of a regular hexagon. 

A
hexagon has 6 sides, so n = 6
Substitute in the formula. 

3. 
The
measure of each exterior angle of a regular polygon is
45°.
How many sides does the polygon have ? 

Set
the formula equal to 45^{0}.
Cross multiply and solve for n.



