The ratio of an interior angle to an exterior angle of a regular polygon is 5 : 2. What is the number of sides of the polygon ?
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Interior angle of polygon of n sides = (n – 2) × 180°/n
Exterior angle of a polygon of n sides = 360°/n
Given, (n – 2) × 180°/n : 360°/n = 5 : 2
=> (n – 2) × 180°/n × 360°/n = 5/2
=> (n – 2)/2 = 5/2
=> 2(n – 2) = 10
=> 2n – 4 = 10
=> 2n = 14
=> n = 7.
Therefore number of sides of the polygon is 7.
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