Question

given $m \parallel n$, find the value of x.

Explanation:

Step1: Identify Angle Relationship

Since \( m \parallel n \) and \( t \) is a transversal, the two angles \( (5x + 24)^\circ \) and \( (6x - 6)^\circ \) are alternate exterior angles. Alternate exterior angles are equal when lines are parallel. So, set the expressions equal:
\( 5x + 24 = 6x - 6 \)

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides:
\( 24 = x - 6 \)

Add 6 to both sides:
\( x = 24 + 6 = 30 \)

Answer:

\( x = 30 \)