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Finding the Interior Angle of a Regular Polygon

(KS2, Year 6)

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

regular polygons interior angles 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?

interior angle of a regular pentagon example

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°.

Lesson Slides

The slider below shows another real example of how to find the interior angle of a regular polygon.

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:

polygons sum of interior angles mini

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.

regular polygons interior angles mini