Find the number of sides of a regular polygon whose exterior angle and interior angle are in the ratio 1 : 5.
Answer & explanation
Correct answer: option 3
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