Question

If the interior angle of a regular polygon is 108°.The polygon has how many sides?

Answer 1

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Answer 2

Given:

The measure of interior angle of a regular polygon is 108°.

To Find:

The number of sides of the polygon.

Solution:

1. It is given that the measure of interior angle of a regular polygon is 108°.

2. According to the properties of geometry, the sum of interior angles of a polygon is equal to [(n-2)180°]/n

=> Sum of interior angles = [(n-2)180°]/n,

=> 108n = 180n - 360, ( Simplify the equation to find the value of n )

=> 180n - 108n = 360,

=> 72n = 360,

=> n = 360/72,

=> n = 5.

3. The polygon has 5 sides.

Therefore, the total sides of the polygon is 5, the polygon with 5 sides is known as pentagon.