What is the measurement of one exterior angle of a regular decagon?

36 degrees

Step-by-step explanation:

A decagon is a 10 sided polygon. We can tell this because the prefix "deca-" stands for ten. To find the exterior angles of a regular polygon you can do 360 divided by the number of sides. Since there are 10 sides on a decagon, the equation is 360/10, which equals 36 degrees.

On the other hand, you can find the interior angles by using a different equation. The sum of the angles in a polygon is equal to 180(n-2) where n is the number of sides. So, a decagon has 1440 degrees. Then, to find the measure of each individual angle divide this number by the number of sides, 10. Thus, each angle is 144 degrees.

You can use this information to check the original answer. The interior angle plus the exterior angle should equal 180. Since 144+36=180, we know that the answer is correct.