Question

two parallel lines ( l ) and ( m ) cut by a transversal. one angle is ( (13x - 21)^circ ), another angle is ( (5x + 75)^circ ).

Explanation:

Step1: Identify the relationship

The angles \((13x - 21)^\circ\) and \((5x + 75)^\circ\) are alternate interior angles, so they are equal.
\[13x - 21 = 5x + 75\]

Step2: Solve for \(x\)

Subtract \(5x\) from both sides:
\[13x - 5x - 21 = 75\]
\[8x - 21 = 75\]

Add 21 to both sides:
\[8x = 75 + 21\]
\[8x = 96\]

Divide both sides by 8:
\[x = \frac{96}{8}\]
\[x = 12\]

Answer:

\(x = 12\)