Question

The exterior angle of a regular polygin is one-third of its interior angle. how many sides has the polygon. Pls answer step by step

Answer 1

Let the interior angle of a regular polygon be x.
Therefore, the exterior angle will be x/3.

exterior angle+ adjacent interior angle = 180°
x/3. + x. = 180°
4x/3. = 180°
x. = 135°

Therefore, the interior angle is 135°.

Let n be the number of sides.
Each interior angle of a regular polygon = (2n -4)*90° / n
135°. =(2n -4) *90° / n
135° n. = 180° n - 360°
180°n - 135°n = 360°
45°n. = 360°
n. = 360° /45°
n. = 8

Ans.= The given regular polygon has 8 sides.