Question

The ratio between the interior angle and the exterior angle of a regular polygon is 2: 1. Find:

(i) each exterior angle of the polygon ;
(ii) number of sides in the polygon.

Answer 1

Interior angle : exterior angle = 2 : 1

Let interior angle = 2x° & exterior angle = x°

∴ 2x° + x° = 180°

3x = 180°

x = 60°

∴ Each exterior angle = 60°

Let no.of. sides = n

`(360°)/"n" = 60°`

n = `(360°)/(60°)`

n = 6

∴ (i) x = 60° (ii) 6