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# Finding the Sum of the Interior Angles of a Polygon

(KS2, Year 6)

## The Lesson

The sum of the interior angles of a polygon is found using the formula:In this formula,

**n**is the number of sides of the polygon. The formula tells you what the interior angles of a polygon add up to.

## How to Find the Sum of the Interior Angles of a Polygon

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

What is the sum of the interior angles of a pentagon?## Step-by-Step:

# 1

Start with the formula:

Sum of interior angles = (n − 2) × 180°

# 2

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

Sum of interior angles = (5 − 2) × 180°
Sum of interior angles = 3 × 180°
Sum of interior angles = 540°

## Answer:

The sum of the interior angles of a pentagon is 540°.## 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?

Any polygon can be split into a number of triangles, each of which has interior angles adding up to 180°.The number of triangles is 2 less than the number of sides and there are there are 180° of interior angles for every triangle:

(n − 2) × 180°

This is why the formula works.
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