Question

The ratio of an external angle and an internal angle of a regular polygon is $1:5$ The number of sides in the polygon is

• A. $12$
• B. $6$
• C. $8$
• D. $10$

Answer 1

The correct option is A $12$

Given ratio of exterior to interior angle of regular polygon is 1:5

Let 'n' be number of sides of polygon

then $\frac{\frac{360}{n}}{\frac{180(n-2)}{n}}=\frac{1}{5}$ (Given)

$\frac{2}{n-2}=\frac{1}{5}\Rightarrow n-2=10\Rightarrow [n=12]$

Hence polygon has 12 sides.