Let's solve the given problem step-by-step.
1. Write down the given angles:
[tex]\[
\angle A = (3x - 4)^\circ
\][/tex]
[tex]\[
\angle B = (2x - 1)^\circ
\][/tex]
2. Use the property of a parallelogram that the sum of any two adjacent angles is [tex]\(180^\circ\)[/tex]:
[tex]\[
\angle A + \angle B = 180^\circ
\][/tex]
Substitute the expressions for [tex]\(\angle A\)[/tex] and [tex]\(\angle B\)[/tex]:
[tex]\[
(3x - 4)^\circ + (2x - 1)^\circ = 180^\circ
\][/tex]
3. Combine the like terms:
[tex]\[
(3x - 4 + 2x - 1)^\circ = 180^\circ
\][/tex]
[tex]\[
(5x - 5)^\circ = 180^\circ
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Add 5 to both sides of the equation:
[tex]\[
5x - 5 + 5 = 180 + 5
\][/tex]
[tex]\[
5x = 185
\][/tex]
Divide by 5:
[tex]\[
x = \frac{185}{5}
\][/tex]
[tex]\[
x = 37
\][/tex]
5. Find the measures of [tex]\(\angle A\)[/tex] and [tex]\(\angle B\)[/tex] by substituting [tex]\(x = 37\)[/tex] into the expressions:
For [tex]\(\angle A\)[/tex]:
[tex]\[
\angle A = 3x - 4
\][/tex]
Substitute [tex]\(x = 37\)[/tex]:
[tex]\[
\angle A = 3(37) - 4
\][/tex]
[tex]\[
\angle A = 111 - 4
\][/tex]
[tex]\[
\angle A = 107^\circ
\][/tex]
For [tex]\(\angle B\)[/tex]:
[tex]\[
\angle B = 2x - 1
\][/tex]
Substitute [tex]\(x = 37\)[/tex]:
[tex]\[
\angle B = 2(37) - 1
\][/tex]
[tex]\[
\angle B = 74 - 1
\][/tex]
[tex]\[
\angle B = 73^\circ
\][/tex]
6. Summary of the solution:
[tex]\[
\angle A = 107^\circ
\][/tex]
[tex]\[
\angle B = 73^\circ
\][/tex]
[tex]\[
x = 37
\][/tex]
Thus, the measures of the angles are [tex]\(\angle A = 107^\circ\)[/tex], [tex]\(\angle B = 73^\circ\)[/tex], and the value of [tex]\(x\)[/tex] is 37.
