To solve for the measure of [tex]\(\angle 2\)[/tex], given that [tex]\(\angle 1\)[/tex] and [tex]\(\angle 2\)[/tex] form a linear pair and are supplementary, follow these steps:
1. Understanding Supplementary Angles:
- Supplementary angles are two angles whose measures add up to [tex]\(180^\circ\)[/tex].
2. Given Information:
- [tex]\(m \angle 1 = -6^\circ\)[/tex]
- [tex]\(m \angle 2 = 5x + 18^\circ\)[/tex]
3. Equation Setup:
- Since [tex]\(\angle 1\)[/tex] and [tex]\(\angle 2\)[/tex] are supplementary, their measures add up to [tex]\(180^\circ\)[/tex]. Thus, we set up the equation:
[tex]\[
m \angle 1 + m \angle 2 = 180^\circ
\][/tex]
- Substituting the given measures:
[tex]\[
-6 + 5x + 18 = 180
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Simplify the equation:
[tex]\[
-6 + 18 + 5x = 180
\][/tex]
[tex]\[
12 + 5x = 180
\][/tex]
- Isolate the term with [tex]\(x\)[/tex]:
[tex]\[
5x = 180 - 12
\][/tex]
[tex]\[
5x = 168
\][/tex]
- Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{168}{5}
\][/tex]
- Simplifying this fraction, we get:
[tex]\[
x = 33.6
\][/tex]
5. Substitute [tex]\(x\)[/tex] back into the expression for [tex]\(m \angle 2\)[/tex]:
- Now that we have the value of [tex]\(x\)[/tex], substitute it back into [tex]\(m \angle 2 = 5x + 18\)[/tex] to find the measure of [tex]\(\angle 2\)[/tex]:
[tex]\[
m \angle 2 = 5 \left(\frac{168}{5}\right) + 18
\][/tex]
[tex]\[
m \angle 2 = 168 + 18
\][/tex]
[tex]\[
m \angle 2 = 186^\circ
\][/tex]
Thus, the measure of [tex]\(\angle 2\)[/tex] is [tex]\(186^\circ\)[/tex]. None of the given options (a, b, c, d) match this value, so there might be an error in the provided options. However, based on the calculations, the correct measure is [tex]\(186^\circ\)[/tex].
