Question

An exterior ongle and interior angle of a regular polygon are in the ratio 3:6. Find the
number of sides in the polygon.​

Answer 1

Answer:

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Step-by-step explanation:

Since, interior angle + exterior angle of any polygon ,at one vertex = 180° & the ratio of these angles = 3:6

=> 3x + 6x = 180

=> 9x = 180

=> x = 20

=> 3x = 3×20=60° & 6x = 6×20=120°

=> Here interior angle has to be 120° as interior angle of any regular polygon can not be less than 60°

Now, we know the formula of each interior angle of a regular polygon = (n-2)180 / n , (where n is the number of sides of the polygon)

=> (n-2)*180 / n = 120

=> 180n - 120n = 360

=> 60n = 360

=> n = 6

So, the regular polygon has 6 equal side.