Let's solve this step-by-step:
Given that [tex]\( \angle A \)[/tex] and [tex]\( \angle B \)[/tex] are corresponding angles formed by a pair of parallel lines cut by a transversal, we know that corresponding angles are equal.
1. Set the measures of the angles equal to each other:
[tex]\[
5x - 4 = 8x - 28
\][/tex]
2. Rearrange the equation to isolate [tex]\( x \)[/tex]. Start by subtracting [tex]\( 5x \)[/tex] from both sides:
[tex]\[
-4 = 3x - 28
\][/tex]
3. Next, add 28 to both sides to further isolate the term involving [tex]\( x \)[/tex]:
[tex]\[
24 = 3x
\][/tex]
4. Finally, divide both sides of the equation by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 8
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 8 \)[/tex].
So, the correct answer is:
[tex]\[ 8 \][/tex]
