Question

The ratio between the exterior angle and the interior angle of a regular polygon is 1:4. Find the number of sides in the 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 = 180°
x/4 + x. = 180°
5x /4. = 180°
x. = 180° * 4/5
= 144°

The interior angle is 144°.
The exterior angle is 36°.

Let n be the number of sides.

n = 360°/ exterior angle
= 360° / 36°
= 10

Ans.= The number of sides of a regular polygon is 10.

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