Sure, let's solve the problem step-by-step.
When parallel lines are cut by a transversal, the corresponding angles are equal. This means that [tex]\( \angle A \)[/tex] is equal to [tex]\( \angle B \)[/tex]. Given:
[tex]\[ m \angle A = (6x - 3)^\circ \][/tex]
[tex]\[ m \angle B = (9x - 24)^\circ \][/tex]
Since [tex]\( \angle A \)[/tex] and [tex]\( \angle B \)[/tex] are corresponding angles, we set them equal to each other:
[tex]\[ 6x - 3 = 9x - 24 \][/tex]
Let's solve this equation for [tex]\( x \)[/tex]:
1. First, we will isolate the terms involving [tex]\( x \)[/tex] on one side of the equation and the constant terms on the other. This means we will subtract [tex]\( 6x \)[/tex] from both sides:
[tex]\[
6x - 3 - 6x = 9x - 24 - 6x
\][/tex]
Simplifying, we get:
[tex]\[
-3 = 3x - 24
\][/tex]
2. Next, we'll add 24 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
-3 + 24 = 3x - 24 + 24
\][/tex]
Simplifying, we get:
[tex]\[
21 = 3x
\][/tex]
3. To solve for [tex]\( x \)[/tex], we divide both sides by 3:
[tex]\[
\frac{21}{3} = \frac{3x}{3}
\][/tex]
Simplifying, we find:
[tex]\[
x = 7
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 7 \)[/tex].
To verify, substitute [tex]\( x = 7 \)[/tex] back into both expressions for [tex]\( m \angle A \)[/tex] and [tex]\( m \angle B \)[/tex]:
[tex]\[ m \angle A = 6(7) - 3 = 42 - 3 = 39^\circ \][/tex]
[tex]\[ m \angle B = 9(7) - 24 = 63 - 24 = 39^\circ \][/tex]
Both values are equal, confirming that our solution is correct.
So, the value of [tex]\( x \)[/tex] is:
[tex]\[ \boxed{7} \][/tex]
