Question

The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides of the polygon.

Answer 1

Let the interior angle be x

Then, the exterior angle is `x/(3)`

∴ `x + x/(3)` = 180°  ...[Interior angle and exterior angle form a linear pair]

⇒ `(4x)/(3)` = 180°

⇒ x = `(3)/(4) xx 180°`
= 135°

∴ Exterior angle

= `(135°)/(3)`
= 45°

Each exterior angle

= `(360°)/"n"`

⇒ `(360°)/"n"` = 45°
⇒ n = 8
∴ the regular polygon has 8 sides.