Certainly! Let's solve this step-by-step:
To begin with, we know that two angles are considered supplementary if their measures add up to [tex]\(180^\circ\)[/tex].
Let the measures of the two angles be as follows:
- The first angle is [tex]\((7x + 2)^\circ\)[/tex].
- The second angle is [tex]\((3x - 2)^\circ\)[/tex].
Since these angles are supplementary, we can set up the following equation:
[tex]\[
(7x + 2) + (3x - 2) = 180
\][/tex]
Next, combine like terms on the left side of the equation:
[tex]\[
7x + 2 + 3x - 2 = 180
\][/tex]
This simplifies to:
[tex]\[
10x = 180
\][/tex]
To solve for [tex]\(x\)[/tex], divide both sides of the equation by 10:
[tex]\[
x = \frac{180}{10}
\][/tex]
So, we find that:
[tex]\[
x = 18
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(18\)[/tex], which corresponds to one of the given choices:
[tex]\[
\boxed{18}
\][/tex]
