To find the measure of [tex]\( m \angle 2 \)[/tex], let's go through the steps systematically:
1. Understand the problem:
[tex]\(\angle 1\)[/tex] and [tex]\(\angle 2\)[/tex] are supplementary angles, which means their measures add up to [tex]\(180^\circ\)[/tex]. We are given:
[tex]\[
m \angle 1 = 7x - 6
\][/tex]
[tex]\[
m \angle 2 = 5x + 18
\][/tex]
2. Set up the equation:
Since the angles are supplementary, the sum of their measures is [tex]\(180^\circ\)[/tex]. Therefore, we can write:
[tex]\[
(7x - 6) + (5x + 18) = 180
\][/tex]
3. Simplify the equation:
Combine like terms:
[tex]\[
7x - 6 + 5x + 18 = 180
\][/tex]
[tex]\[
12x + 12 = 180
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Isolate [tex]\(x\)[/tex] by first subtracting 12 from both sides:
[tex]\[
12x = 168
\][/tex]
Then divide both sides by 12:
[tex]\[
x = 14
\][/tex]
5. Find [tex]\(m \angle 2\)[/tex]:
Substitute [tex]\(x = 14\)[/tex] back into the expression for [tex]\(m \angle 2\)[/tex]:
[tex]\[
m \angle 2 = 5x + 18
\][/tex]
[tex]\[
m \angle 2 = 5(14) + 18
\][/tex]
[tex]\[
m \angle 2 = 70 + 18
\][/tex]
[tex]\[
m \angle 2 = 88
\][/tex]
Thus, the measure of [tex]\( m \angle 2 \)[/tex] is [tex]\(88^\circ\)[/tex].
The correct answer is:
d) [tex]\(88^\circ\)[/tex]
