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Question

Question 140
The ratio between exterior angle and interior angle of a regular polygon is 1 : 5. Find the number of sides of the polygon.

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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=180x=1806x=Exterior angle=30
The number of sides
=360Exterior angle
=36030
=12

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