The problem asks us to find the measure of an exterior angle of a regular decagon.

1. Problem Description

The problem asks us to find the measure of an exterior angle of a regular decagon.

2. Solution Steps

A decagon is a polygon with 10 sides. A regular decagon has 10 equal sides and 10 equal interior angles.

The sum of the exterior angles of any polygon is always 360 degrees. For a regular polygon, all the exterior angles are equal.

Let $n$ be the number of sides of the regular polygon, which is also the number of exterior angles.

Let $x$ be the measure of one exterior angle of a regular polygon.

The sum of the exterior angles is $n \times x = 360$ degrees.

Therefore, the measure of one exterior angle of a regular n-sided polygon is given by

$x = \frac{360}{n}$

In this problem, the polygon is a regular decagon, so $n = 10$.

$x = \frac{360}{10} = 36$

3. Final Answer

The measure of the exterior angle of a regular decagon is 36 degrees.