Question

The number angle of a regular polygon is double the exterior angle. Find the number of sides of the polygon.

Answer 1

Let the exterior angle be x
Then, the interior angle is 2x
x + 2x = 180°  ...[Interior angle and exterior angle form a linear pair]

⇒ 3x = 180°

⇒ x = `(180°)/(3) xx 60°`
∴ Exterior angle = 60°
Each exterior angle

= `(360°)/"n"`

⇒ `(360°)/"n"` = 60°
⇒ n = 6
∴ the regular polygon has 6 sides.