An interior angle of a regular polygon has a measure of 108°. What type of polygon is it?

Solution:

It is given that

One interior angle of a regular polygon = 108°

The sum of interior angles of a regular polygon = (n - 2) × 180°

The interior angle of a regular polygon = [(n - 2) × 180°]/n

By equating both we get

108 = [(n - 2) × 180°]/n

By further simplification

108n = 180n - 360

180n - 108n = 360

So we get

72n = 360

n = 5

Therefore, it is a 5 sided polygon known as pentagon.

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An interior angle of a regular polygon has a measure of 108°. What type of polygon is it?

Summary:

An interior angle of a regular polygon has a measure of 108°. It is a 5 sided polygon known as pentagon.