Find the number of sides of a regular polygon whose exterior angle and interior angle are in the ratio 1 : 5.

12

The correct answer is Option (3) → 12

Sum of Exterior angles (E) of a regular polygon = 360º

Assume number of sides be n

Also, sum of internal angles (I) of a regular polygon = (n-2) 180º

Given, E:I :: 1:5

\(\frac{360º}{(n-2)180º}\) = \(\frac{1}{5}\)

(n-2)180º = 360º × 5

n-2 = 10

n = 12

Thus, number of sides of regular polygon is 12