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