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

# How to Find the Exterior Angle of a Regular Polygon

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

**Question:**What is the exterior angle of a regular octagon?

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

An octagon has 8 sides. n = 8.

**Step 2:**Divide 360° by n, the number of sides.

360° ÷ 8 = 45°.

The exterior angle of a regular octagon is 45°.

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

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

##### Interactive Test

**show**

##### Note

**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.

This is why the formula works.