Given that a pair of parallel lines is cut by a transversal, the angles [tex]\(\angle A\)[/tex] and [tex]\(\angle B\)[/tex] are corresponding angles. Therefore, they are equal. We are given the measures of these angles as:
[tex]\[ m \angle A = (4x - 2)^\circ \][/tex]
[tex]\[ m \angle B = (6x - 20)^\circ \][/tex]
Since the angles are corresponding and thus equal, we can set up the following equation:
[tex]\[ 4x - 2 = 6x - 20 \][/tex]
To solve for [tex]\(x\)[/tex], we follow these steps:
1. Subtract [tex]\(4x\)[/tex] from both sides of the equation:
[tex]\[ -2 = 2x - 20 \][/tex]
2. Add 20 to both sides of the equation:
[tex]\[ 18 = 2x \][/tex]
3. Divide both sides by 2:
[tex]\[ x = 9 \][/tex]
Therefore, the value of [tex]\(x\)[/tex] is:
[tex]\[ x = 9 \][/tex]
Hence, the correct answer is:
[tex]\[ 9 \][/tex]
