To find the value of [tex]\( x \)[/tex], let's analyze the given angles [tex]\( m \angle A \)[/tex] and [tex]\( m \angle B \)[/tex].
Given:
[tex]\[ m \angle A = (4x - 2)^\circ \][/tex]
[tex]\[ m \angle B = (6x - 20)^\circ \][/tex]
Since the two angles are corresponding angles in parallel lines cut by a transversal, they are equal. Therefore, we can set up the equation:
[tex]\[ 4x - 2 = 6x - 20 \][/tex]
Next, let's solve this equation step-by-step:
1. First, we will isolate the variable [tex]\( x \)[/tex] by moving all the terms involving [tex]\( x \)[/tex] to one side of the equation and the constant terms to the other side. To do this, subtract [tex]\( 4x \)[/tex] from both sides:
[tex]\[ -2 = 2x - 20 \][/tex]
2. Next, add 20 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ -2 + 20 = 2x \][/tex]
[tex]\[ 18 = 2x \][/tex]
3. Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{18}{2} \][/tex]
[tex]\[ x = 9 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 9 \)[/tex].
