The ratio of exterior angle to the interior angle of a regular polygon is 1:4. Find the number of sides of the polygon?

Let the interior angle of the regular polygon be x.

Then the exterior angle is x/4.

Exterior angle + adjacent interior angle = 180°

x = 144°

The interior angle is 144°

The exterior angle is 36°

In a regular polygon the exterior angle is equal and the sum of 360°.

Let n be the number of sides

So, the number of sides in a regular polygon is 10.