Sure! Let's solve the problem step-by-step.
We are given the measure of angle 5 as [tex]\( (11x - 14)^\circ \)[/tex] and the value of [tex]\( x \)[/tex] is 6. First, we need to find the measure of angle 5 by substituting [tex]\( x = 6 \)[/tex] into the given expression.
Step 1: Calculate the measure of angle 5
[tex]\[
\text{Measure of angle 5} = 11x - 14
\][/tex]
Substitute [tex]\( x = 6 \)[/tex]:
[tex]\[
\text{Measure of angle 5} = 11(6) - 14 = 66 - 14 = 52^\circ
\][/tex]
Now, let's evaluate each of the given expressions for the measure of angle 2 to see which ones could match the measure of angle 5.
Step 2: Check the given expressions
1. Expression 1: [tex]\( (8x + 4)^\circ \)[/tex]
[tex]\[
8x + 4 = 8(6) + 4 = 48 + 4 = 52^\circ
\][/tex]
2. Expression 2: [tex]\( (9x + 2)^\circ \)[/tex]
[tex]\[
9x + 2 = 9(6) + 2 = 54 + 2 = 56^\circ
\][/tex]
3. Expression 3: [tex]\( (20x + 8)^\circ \)[/tex]
[tex]\[
20x + 8 = 20(6) + 8 = 120 + 8 = 128^\circ
\][/tex]
4. Expression 4: [tex]\( (18x + 20)^\circ \)[/tex]
[tex]\[
18x + 20 = 18(6) + 20 = 108 + 20 = 128^\circ
\][/tex]
Step 3: Determine which expressions match the calculated measure of angle 5
From these evaluations, we see that:
- [tex]\( (8x + 4)^\circ \)[/tex] = 52°
- [tex]\( (9x + 2)^\circ \)[/tex] ≠ 52°
- [tex]\( (20x + 8)^\circ \)[/tex] ≠ 52°
- [tex]\( (18x + 20)^\circ \)[/tex] ≠ 52°
Therefore, the only expression that could represent the measure of angle 2 is [tex]\( (8x + 4)^\circ \)[/tex], which matches the measure of angle 5.
So, the correct expression that could represent the measure of angle 2 is [tex]\( (8x + 4)^\circ \)[/tex].
