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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:

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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.