How to Find the Exterior Angle of a Regular Polygon
Finding the Exterior Angle of a Regular Polygon
Each exterior angle of a regular polygon is given by the formula:
In this formula, n is the number of sides of the regular polygon.
How to Find the Exterior Angle of a Regular Polygon
Finding the exterior angle of a regular polygon is easy.
Question
What is the exterior angle of a regular octagon?
Step-by-Step:
1
Start with the formula:
Exterior angle = 360° ⁄ n
Don't forget: / means ÷.
2
Substitute the number of sides into the formula.
An octagon has 8 sides. In our example, n = 8.
Exterior angle = 360° ÷ 8
Exterior angle = 45°
Answer:
The exterior angle of a regular octagon is 45°.
See Also
What is an angle?Interactive Test
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Here's a second test on finding the exterior angle of a regular polygon
Here's a third test on finding the exterior angle of a regular polygon
Note
Why Does the Formula Work?
The sum of the exterior angles of a polygon is 360°.
There are as many exterior angles as there are sides, n, and they are all equal.
The sum is divided by n to find each exterior angle.
In this formula, n is the number of sides of the polygon.
This is why the formula works.