The ratio of an interior angle to the exterior angle of a regular polygon is 4 : 1. The number of sides of the polygon is:

Correct option is B

Given:

The ratio of the interior angle to the exterior angle of a regular polygon is 4 : 1. 

Formula Used: 

Exterior angle of polygon = $$\frac{360\degree}{n}$$​​

Solution:

Interior angle : Exterior angle = 4 : 1

Let interior angle = 4$$x^\circ$$ & exterior angle = $$x^\circ$$ 

4$$x^\circ$$ + $$x^\circ$$ = $$180^\circ$$ 

5x = $$180^\circ$$

x = $$\frac{180^\circ}{5}$$ = $$36^\circ$$ 

Let no. of side = n

​$$\frac{360^\circ}{n}= 36^\circ$$ 

n = $$\frac{360^\circ}{36^\circ}$$ 

n = 10

The number of sides of the polygon is: 10