Finding the Exterior Angle of a Regular Polygon
(KS2, Year 6)

The Lesson

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°.

Lesson Slides

The slider below shows another real example of how to find the exterior angle of a regular octagon. Open the slider in a new tab

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.
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See Also

What is an angle?