How to Find the Interior Angle of a Regular Polygon

Finding the Interior Angle of a Regular Polygon

Each interior angle of a regular polygon is found using the formula:

In this formula, n is the number of sides of the regular polygon.

How to Find the Interior Angle of a Regular Polygon

Finding the interior angle of a regular polygon is easy.

Question

What is the interior angle of a regular pentagon?

Step-by-Step:

1

Start with the formula:

Interior angle = (n − 2) × 180° ⁄ n

Don't forget: / means ÷.

2

Substitute the number of sides into the formula.

A pentagon has 5 sides. In our example, n = 5.

Interior angle = (5 − 2) × 180° ⁄ 5

Interior angle = 3 × 180° ÷ 5

Interior angle = 540° ÷ 5

Interior angle = 108°

Answer:

The interior angle of a regular pentagon is 108°.

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See Also

What is an angle?