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