If the exterior angle of a regular polygon is one-fifth of its interior angle. How many sides does the polygon have?

We have a regular polygon.

Let the interior angle of the regular polygon be x.

Then, the exterior angle will be given by

Exterior Angle = (180 – x) [∵ Sum of an interior angle and exterior angle is equal to 180°]

According to the question, exterior angle of a regular polygon is one-fifth of its interior angle. We can write as,

⇒ 900 – 5x = x

⇒ 900 = 5x + x

⇒ 900 = 6x

⇒ x = 150

⇒ Each interior angle = 150°

The number of sides in a regular polygon is given by

⇒ (n – 2) × 180 = 150n

⇒ 6 (n – 2) = 5n

⇒ 6n – 12 = 5n

⇒ 6n – 5n = 12

⇒ n = 12

Therefore, the number of sides = 12