Question

In a certain regular polygon, the measure of each interior angle is four times the measure of each exterior angle. Find the number of sides in this regular polygon.

Answer 1

Answer: 10

Explanation:

Let x be the measure of each exterior angle ( in degrees) .

Then the measure of each interior angle ( in degrees) = 4x

We know that the sum of exterior angle and interior angle = 180 degrees.

i.e. x+4x= 180

i.e. 5x = 180

i.e. x= 36 [Divide both sides by 5]

i.e. The measure of each exterior angle= 36°

Also, Sum all exterior angles is 360° .

Number of sides in regular polygon = 360° ÷ (Measure of each exterior angle)

= 360° ÷ 36

=10

Therefore , the number of sides in this regular polygon= 10