Sure, let's solve this step-by-step.
We are given that there are two parallel lines cut by a transversal and that the measure of angles [tex]\( \angle A \)[/tex] and [tex]\( \angle B \)[/tex] are given by:
[tex]\[ m \angle A = (5x - 4)^\circ \][/tex]
[tex]\[ m \angle B = (8x - 28)^\circ \][/tex]
In the case of parallel lines being cut by a transversal, certain angles are equal to each other. Specifically, alternate interior angles or corresponding angles are equal. Assuming [tex]\( \angle A \)[/tex] and [tex]\( \angle B \)[/tex] are such pairs, we can say:
[tex]\[ 5x - 4 = 8x - 28 \][/tex]
Now let's solve the equation step-by-step.
1. Start with the equation:
[tex]\[ 5x - 4 = 8x - 28 \][/tex]
2. To isolate the variable [tex]\( x \)[/tex], first get all the [tex]\( x \)[/tex]-terms on one side of the equation. Subtract [tex]\( 5x \)[/tex] from both sides:
[tex]\[ -4 = 3x - 28 \][/tex]
3. Next, isolate the constant term by adding 28 to both sides:
[tex]\[ -4 + 28 = 3x \][/tex]
[tex]\[ 24 = 3x \][/tex]
4. Finally, solve for [tex]\( x \)[/tex] by dividing both sides by 3:
[tex]\[ x = \frac{24}{3} \][/tex]
[tex]\[ x = 8 \][/tex]
Thus, the value of [tex]\( x \)[/tex], which satisfies the equation given the conditions, is:
[tex]\[ x = 8 \][/tex]
So, the correct answer is:
[tex]\[ 8 \][/tex]
