Question

two vertical parallel lines (l and m) are cut by a transversal, forming angles labeled ((5x + 7)^circ) and ((8x - 71)^circ).

Explanation:

Step1: Identify the relationship

Since lines \( l \) and \( m \) are parallel, the two angles \( (5x + 7)^\circ \) and \( (8x - 71)^\circ \) are alternate interior angles, so they are equal.
\[
5x + 7 = 8x - 71
\]

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides:
\[
7 = 3x - 71
\]
Add 71 to both sides:
\[
7 + 71 = 3x
\]
\[
78 = 3x
\]
Divide both sides by 3:
\[
x = \frac{78}{3} = 26
\]

Answer:

\( x = 26 \)