Question

The measure of an interior angle of a regular polygon is 108°. What is the name of the
regular polygon? Justify.

Answer 1

Answer:

Pentagon

Step-by-step explanation:

Given that, one interior angle is 108 degrees.

Sum of interior angles of a regular polygon = (n − 2) × 180°

Interior angle of a regular polygon = [(n − 2) × 180°] / n

108° = [(n − 2) × 180°]/n

108n = 180n - 360

72n = 360

n = 5

A 5-sided polygon is called a pentagon.

Hence, if an interior angle of a regular polygon measures 108°, then it is a pentagon (a 5-sided polygon).

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Answer 2

Answer:

Since Interior angle is 108 degree

Exterior angle will be 180-108 degree = 72 degree

Now number of sides the polygon has = 360/72 = 5

A 5 sided polygon is called a pentagon.

So your answer is Pentagon.