A pair of parallel lines is cut by a transversal.

If [tex]m \angle A = (4x - 2)^{\circ}[/tex] and [tex]m \angle B = (6x - 20)^{\circ}[/tex], what is the value of [tex]x[/tex]?

A. 34
B. 20.2
C. 11.2
D. 9



Answer :

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]