To find the value of [tex]\( x \)[/tex], follow these detailed steps:
1. Understanding the properties of exterior angles in polygons:
- The sum of all exterior angles of any polygon is always [tex]\( 360^\circ \)[/tex], regardless of the number of sides.
2. Identify the type of polygon:
- In this problem, we have a regular pentagon, which means it has 5 sides.
3. Calculate the measure of one exterior angle:
- For a regular pentagon, since all sides and angles are equal, the measure of each exterior angle is found by dividing the total sum of exterior angles by the number of sides.
- Measure of one exterior angle of a regular pentagon [tex]\( = \frac{360^\circ}{5} \)[/tex].
4. Compute the measure of one exterior angle:
- [tex]\( \frac{360^\circ}{5} = 72^\circ \)[/tex].
5. Relate this to the given information:
- According to the problem, one exterior angle of the pentagon is [tex]\( 2x^\circ \)[/tex].
- So, we set up the equation [tex]\( 2x = 72 \)[/tex].
6. Solve for [tex]\( x \)[/tex]:
- [tex]\( x = \frac{72}{2} = 36 \)[/tex].
Therefore, the value of [tex]\( x \)[/tex] is:
[tex]\[ x = 36 \][/tex]
So, the correct answer is [tex]\( \boxed{36} \)[/tex].
