What formula gives the measure of a single exterior angle of a regular polygon with n sides?

To find the measure of a single exterior angle of a regular polygon, the correct approach is to use the relationship between the total sum of the exterior angles and the number of sides. In any polygon, the sum of all exterior angles is always 360 degrees, regardless of the number of sides.

Since a regular polygon has all its exterior angles equal, the measure of one exterior angle can be calculated by dividing the total sum of the exterior angles by the number of sides, ( n ). Therefore, the formula to find a single exterior angle is:

[ \text{Exterior angle} = \frac{360}{n} ]

This means that if you take a polygon with ( n ) sides, the measure of each exterior angle will be ( 360 ) degrees divided by ( n ).

In contrast, other options do not represent the correct measure of a single exterior angle. For instance, ( \frac{180(n-2)}{n} ) actually calculates the measure of a single interior angle of a regular polygon, while ( 180n ) and ( \frac{180}{n} ) do not correctly relate to the exterior angle measure. Therefore, the formula ( \frac{360}{n