Question

The ratio between interior and exterior angle of a regular polygon is 1:4. Find the number of sides of 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 $={180}^0$

$\frac{X}{4}+X={180}^0$

$\frac{5X}{4}={180}^0$

$X={180}^0\times \frac{4}{5}$

$={144}^0$

the interior angle is ${144}^0$

the exterior angle is ${36}^0$

$n=\frac{{360}^0}{exteriorangle}$

$=\frac{{360}^0}{{36}^0}=10$

The number of sides of a regular polygon is $10.$