Question

The ratio between an exterior angle and the interior angls of a regular polygon is 1:8 . Find the no. of sides in a polygon.​

Answer 1

let the interior angle of the regular polygon be X.

therefore, the exterior angle is X/4.

Exterior angle + adjacent interior angle =1800 

4X+X=1800

45X=1800

X=1800×54

=1440

the interior angle is 1440

the exterior angle is 360

n=exteriorangle3600

=3603600=10

The number of sides of a regular polygon is 10.

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