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