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Question

The sum of exterior angles of a polygon is one-third of the sum of interior angles. Find the number of sides in the polygon.


A

6

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B

5

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C

8

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D

10

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Solution

The correct option is C

8


Sum of exterior angles of a polygon is 360o.

Let the sum of interior angles be x.

13×x = 360o

x = 360o×3

= 1080o

Sum of interior angles = (2n-4) × 90o, where n is number of sides in polygon

(2n-4) × 90o = 1080o

(2n-4) × 90o = (90 × 12)o

(2n-4) = 12

n = 8

Number of sides in the given polygon is 8.


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