Sure, let's break down the problem step-by-step.
1. Understanding the problem:
- We know that we're dealing with a regular pentagon (a polygon with 5 equal sides and 5 equal angles).
- We are given that one exterior angle of this pentagon is [tex]\(2x\)[/tex] degrees.
- We need to find the value of [tex]\(x\)[/tex].
2. Properties of a regular polygon:
- The sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides.
- For a regular pentagon, each exterior angle will be equal since all sides and angles are equal.
3. Calculate the measure of one exterior angle in a regular pentagon:
- A regular pentagon has 5 sides.
- The measure of each exterior angle is obtained by dividing the total sum of the exterior angles by the number of sides:
[tex]\[
\text{Measure of one exterior angle} = \frac{360^\circ}{5} = 72^\circ
\][/tex]
4. Setting up the equation:
- We know from the problem that this exterior angle measures [tex]\(2x\)[/tex] degrees.
- Therefore, we can set up the equation:
[tex]\[
2x = 72^\circ
\][/tex]
5. Solving for [tex]\(x\)[/tex]:
- Divide both sides of the equation by 2:
[tex]\[
x = \frac{72^\circ}{2} = 36^\circ
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(36\)[/tex] degrees.
So, the correct answer is [tex]\(\boxed{36}\)[/tex].
