Question

EACH interior angle of a regular polygon has a measure of 108 degrees. Find the number of sides the polygon has

Answer 1

Given,

Value of each interior angle of a regular polygon = 108°

To find,

Number of sides of the polygon.

Solution,

Let, the total number of sides of a regular polygon = n

Sum of the interior angles of a regular polygon

= n×108°

According to the formula of the sum of the internal angles,

Sum of the interior angles of a regular polygon

= (n-2)×180°

If we compare the two values then we get the following mathematical equation,

108n = (n-2)×180

108n = 180n-360

180n-360 = 108n

180n-108n = 360

72n = 360

n = 5

Hence, number of sides of the regular polygon is 5.

Answer 2

Given: Each interior angle of a regular polygon has a measure of 108 degrees.

To find: Number of sides the polygon has

Solution:

Let the number of sides of the polygon be 'n'

The measure of each exterior angle = (180° - 108°) = 72°

Also, the measure of each exterior angle = $\frac{360}{n}$

⇒ $\frac{360}{n} = 72$

⇒$n=\frac{360}{72}=5$

Therefore, the given polygon has five sides.