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# Finding the Interior Angle of a Regular Polygon

(KS2, Year 6)

## The Lesson

Each interior angle of a regular polygon is found using the formula:In this formula,

**n**is the number of sides of the regular polygon.

## How to Find the Interior Angle of a Regular Polygon

Finding the interior angle of a regular polygon is easy.## Question

What is the interior angle of a regular pentagon?## Step-by-Step:

# 1

Start with the formula:

Interior angle = (n − 2) × 180° ⁄ n

**Don't forget:**/ means ÷.# 2

Substitute the number of sides into the formula.
A pentagon has 5 sides. In our example, n = 5.

Interior angle = (5 − 2) × 180° ⁄ 5
Interior angle = 3 × 180° ÷ 5
Interior angle = 540° ÷ 5
Interior angle = 108°

## Answer:

The interior angle of a regular pentagon is 108°.## What Is a Polygon?

A polygon is a 2-dimensional shape with straight sides.## What Are the Interior Angles of a Polygon?

The interior angles of a polygon are the angles between two sides, inside the shape.## Why Does the Formula Work?

The sum of the interior angles of a polygon is given by the formula:In this formula,

**n**is the number of sides of the polygon. In a regular polygon, the interior angles are all equal, and there are as many as there are sides,

**n**. So the sum of the interior angles is shared out equally between the

**n**sides. The sum is divided by

**n**to find each interior angle.

This is why the formula works.

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