If the ratio of an external angle and an internal angle of a regular polygon is 1 : 5, then what is the number of sides in the polygon?

12

We have,

The ratio between exterior angle and interior angle of a regular polygon = 1 : 5.

Let the interior angle be 5a and the exterior angle be a.

We know that,

Exterior angle = 180° - interior angle.

a = 180° - 5a

Now, a + 5a = 180°

6a = 180°

a = 30°

Exterior angle = 30°.

The number of sides of a polygon = 360°/measure of exterior angle

= 360°/30° = 12