Question 185

The ratio of each interior angle to each exterior angle of a regular polygon is 3 : 1. The number of sides of the polygon is

Solution

Let the number of sides in the polygon be $$n$$

Each interior angle of a polygon = $$\frac{(n-2)\times180}{n}$$

and each exterior angle of a polygon = $$\frac{360}{n}$$

Acc to ques :

=> $$\frac{\frac{(n-2)\times180}{n}}{\frac{360}{n}} = \frac{3}{1}$$

=> $$\frac{n-2}{2} = \frac{3}{1}$$

=> $$n - 2 = 6$$

=> $$n = 8$$

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