# If the exterior angle in a polygon is 12 degrees what is the number of sides?

Mar 6, 2017

May be $30$ sides, but you need additional information.

#### Explanation:

You cannot find with the given information. The reason is that the only that is sure is that sum of all exterior angles of any polygon is always ${360}^{\circ}$.

As one angle is ${12}^{\circ}$, only thing you can say is that sum of remaining angles is ${360}^{\circ} - {12}^{\circ} = {348}^{\circ}$.

You do not know about other angles and number of sides could be any number. For example, if other angles are ${1}^{\circ}$ each, we may have $349$ sides (this means $348$ angles of ${1}^{\circ}$ and one of ${12}^{\circ}$) and if each off other angle is ${6}^{\circ}$, number of sides could be $59$ (this means $58$ angles of ${6}^{\circ}$ and one of ${12}^{\circ}$).

However, if we have added information that the polygon is a regular polygon , this means all interior as well as exterior angles would be equal. Then number of sides then would be $\frac{{360}^{\circ}}{{12}^{\circ}} = 30$.