Exterior Angle
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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) =

 

Examples


1.

Find the sum of the exterior angles of:
a) a pentagon Answer:  3600
b) a decagon Answer:  3600
c) a 15 sided polygon Answer:  3600
d) a 7 sided polygon Answer:  3600

 

 

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 450.
Cross multiply and solve for n.