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Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1: 5.

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answer is B.

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Detailed Solution

It is given that exterior and interior angles are in the ratio 1: 5.
Let the exterior angle is

x °

. Then interior angle will be

5 x °

.
Sum of an interior and exterior angle with a common vertex of a polygon is

180 °

.
Equate the sum of given interior and exterior angles with a common vertex is

180 °

x ° + 5 x ° = 180 ° ⇒ 6 x ° = 180 ° ⇒ x ° = 30 °

Here, the exterior angle = 30

°

and sum of all interior angles =

360 °

.
Also, we know that,
Number of sides

×

exterior angle = sum of exterior angles

⇒ Number of sides × 30 ° = 360 ° ⇒ Number of sides = 12

Hence, the correct option is 2.

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