# How to Find the Interior Angle of a Regular Polygon (Mathematics Lesson)

# How to Find the Interior Angle of a Regular Polygon

Each interior angle of a regular polygon is given by the formula:# A Real Example of How to Find the Interior Angle of a Regular Polygon

**Question:**What is the interior angle of a regular pentagon?

**Step 1:**Find n, the number of sides.

A pentagon has 5 sides. n = 5.

**Step 2:**Subtract 2.

5 - 2 = 3.

**Step 3:**Multiply by 180°.

3 × 180° = 540°.

**Step 4:**Divide by n, the number of sides.

540° ÷ 5 = 108°.

The interior angle of a regular pentagon is 108°.

# Another Real Example of How to Find the Interior Angle of a Regular Polygon

The slider below shows a real example of how to find the interior angle of a regular polygon:##### Curriculum

##### Interactive Test

**show**

##### Note

**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:

where

**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.