Question

The ratio of exterior angles and interior angle of a polygon is 1:4, then find the
perimeter of the polygon if it side is ‘a’ cm long.

Answer 1

Answer:

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

Each interior angle of a regular polygon = n180o(n−2)  where n= number of sides of polygon

Each exterior angle of a regular polygon = n360o 

According to question,

n360o:n180o(n−2)=1:4

=>(n−2)2=41

=>n−2=8

=>n=10

Number of sides of the polygon =10

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