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°.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.
This page was written by Stephen Clarke.
You might also like...
geometryunderstanding the exterior angles of a polygonunderstanding the sum of an interior and exterior angle of a polygon is 180°trigonometry curriculum
Help Us Improve Mathematics Monster
- Do you disagree with something on this page?
- Did you spot a typo?
Find Us Quicker!
- When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add #mm to your search term.
Share This Page
If you like Mathematics Monster (or this page in particular), please link to it or share it with others.
If you do, please tell us. It helps us a lot!
Create a QR Code
Use our handy widget to create a QR code for this page...or any page.
Worksheet
This test is printable and sendable
