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.

Question

asked Aug 19, 2021 17.0k views

1 Answer

Driscoll · Answer 1 · 2021-08-24T22:15:00+0000

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