Exterior Angle
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) = \(\frac { 360 }{ n } \)
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.
