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How to Find the Exterior Angle of a Regular Polygon (Mathematics Lesson)

How to Find the Exterior Angle of a Regular Polygon

Each exterior angle of a regular polygon is given by the formula:

A Real Example of How to Find the Exterior Angle of a Regular Polygon

Question: What is the exterior angle of a regular octagon?



Step 1: Find n, the number of sides.
An octagon has 8 sides. n = 8.

Step 2: Divide 360° by n, the number of sides.
360° ÷ 8 = 45°.

The exterior angle of a regular octagon is 45°.

Another Real Example of How to Find the Exterior Angle of a Regular Polygon

The slider below shows a real example of how to find the exterior angle of a regular polygon:

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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.



This is why the formula works.