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Question
Each exterior angle of a regular polygon is `(1)/"P" `times of its interior angle. Find the number of sides in the polygon.
Solution
Each interior angle of a regular polygon of n sides = `(("n" - 2) xx 180°)/"n"`
Each interior angle of a regular polygon of n sides = `(360°)/"n"`
Now,
`(360°)/"n" = (1)/"p" xx (("n" - 2) xx 180°)/"n"`
360° = `(1)/"p" xx ("n" - 2) xx 180°`
⇒ n = 2 = `"p" xx (360°)/(180°)`
⇒ n - 2 = 2p
⇒ n = 2p + 2
⇒ n = 2(p + 1)
Thus, the number of sides of a goven regular polygon is 2(p + 1).
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