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: 10

Step-by-step 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