When two parallel lines are intersected by a transversal, the corresponding angles are equal. In this case, angles [tex]\(\angle A\)[/tex] and [tex]\(\angle B\)[/tex] are corresponding angles. Therefore, we can set their measures equal to each other and solve for [tex]\(x\)[/tex].
Given:
[tex]\[ m \angle A = (6x - 3)^\circ \][/tex]
[tex]\[ m \angle B = (9x - 24)^\circ \][/tex]
Since these are corresponding angles, we can write the equation:
[tex]\[ 6x - 3 = 9x - 24 \][/tex]
To find [tex]\(x\)[/tex], follow these steps:
1. Arrange the equation:
[tex]\[ 6x - 3 = 9x - 24 \][/tex]
2. Subtract [tex]\(6x\)[/tex] from both sides to isolate [tex]\(x\)[/tex] terms on one side:
[tex]\[ -3 = 3x - 24 \][/tex]
3. Add 24 to both sides to move the constant term to the other side:
[tex]\[ 21 = 3x \][/tex]
4. Divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{21}{3} \][/tex]
[tex]\[ x = 7 \][/tex]
Thus, the value of [tex]\(x\)[/tex] is 7.
