Question

If each interior angle of a regular polygon is 108 degree

. Find the measure of each exterior
angle and number of sides in it.

Answer 1

As per the data given in the question,

We have to determine the measurement of each exterior angle of polygons and the number of sides.

As per question,

It is given that,

Interior angle of a regular polygon=108°

We know that,

The sum of interior and exterior angle of a polygons is equal to 180 degree.

So,

$108^0+x^0 = 180^0\\=>x^0 = 180^0-108^0\\=>x^0 = 72^0$

So, measurement of each exterior angle will be 72 degree.

The formula for the interior angle of a regular polygon of " n" sides are,

$=[\frac{(n-2)}{n}]\times 180^0\\=[\frac{(n-2)}{n}]\times 180^0=108^0\\=>\frac{(n-2)}{n}=\frac{108}{180}\\=>\frac{(n-2)}{n}=\frac{3}{5}$

on applying cross multiplication,

We will get,

$=>5(n-2)=3n\\=>5n-10=3n\\=>5n-3n=10\\=>2n=10\\=>n=10/2\\=>n=5$

Hence, total number of sides in the given regular polygon will be 5

Answer 2

From the given data,

We have to find the value of the measurement of each exterior angle of polygons and the number of sides.

From question,

It is given that,

Interior angle of a regular polygon=108°

As we know that,

The sum of interior and exterior angle of a polygons is equal to 180 degree.

So,

So, measurement of each exterior angle will be $=180^0-108^0$ = 72 degree.

As we have,

$\frac{n-2}{n}\times 180=108\\\frac{n-2}{n}=\frac{108}{180}\\=>\frac{n-2}{n} = \frac{3}{5}\\=>n -2 = 3\\=>n = 5$

We will get,

Hence, total number of sides in the given regular polygon will be 5