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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:

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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.