Question

The exterior angle of a regular polygon is one-fifth of its interior angle. How many sides
the polygon has?

Answer 1

let the interior angle be x

∴ $\frac{x}{1}$= $\frac{x}{5}$

∴  $\frac{5x+x}{5}$=180

∴ 6x=180x5

∴ x=$\frac{900}{6}$

∴ x=150

therefore the exterior angle 30

∴ 360/30

∴12 sides