Question

The ratio between exterior angle and interior angle of a regular polygon is 1:5. Find the number of sides of the polygon.

Answer 1

Let the exterior angle and interior angle be x and 5x, respectively.

Then, x + 5x = 180°   ...[∵ Exterior angle and corresponding interior angle are supplementary]

⇒ 6x = 180°

⇒ x = `180^circ/6`

⇒ x = 30°

∴ The number of sides = `360^circ/"Exterior angle"`

= `360^circ/30^circ`

= 12