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# 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°.## 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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