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Question

The ratio between the exterior angle and interior angle of a regular polygon is 1:4. Find the number of sides in the polygon.

A
8
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B
9
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C
10
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D
11
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Solution

The correct option is C 10
The ratio between the exterior angle and interior angle of a regular polygon is 1:4

Each interior angle of a regular polygon = 180o(n2)n where n= number of sides of polygon

Each exterior angle of a regular polygon = 360on

According to question,

360on:180o(n2)n=1:4

=>2(n2)=14

=>n2=8

=>n=10

Number of sides of the polygon =10

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