Question

27. The ratio between an exterior angle and the
interior angle of a regular polygon is 1 : 5.
Find its number of sides.​

Answer 1

Let the external angle = 1x or x

Le the interior angle = 5x

We know, sum of interior angle and exterior angle = 180

So,here

1x + 5x = 180

6x = 180

x = 180/6= 30°

Therefore, exterior angle = 30°

We know, no. of sides = 360/exterior angle

= 360/30= 12 sides.

Therefore, the polygon has 12 sides.

HAVE A NICE DAY!