# How to Find the Sum of the Interior Angles of a Polygon (Mathematics Lesson)

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

The sum of the interior angles of a polygon is given by the formula:where

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

The formula tells you what the interior angles of a polygon add up to.

# A Real Example of How to Find the Sum of the Interior Angles of a Polygon

**Question:**What is the sum of the interior angles of a 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°.

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

# Another Real Example of How to Find the Sum of the Interior Angles of a Polygon

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

##### Interactive Test

**show**

##### Note

**WHAT IS 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.