Question

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

Explanation:

Step1: Identify Alternate Interior Angles

Since \( m \parallel n \) and \( t \) is a transversal, the angles \( (3x - 15)^\circ \) and \( (x + 7)^\circ \) are alternate interior angles. Alternate interior angles are equal when lines are parallel. So, we set up the equation:
\( 3x - 15 = x + 7 \)

Step2: Solve for \( x \)

Subtract \( x \) from both sides:
\( 3x - x - 15 = 7 \)
\( 2x - 15 = 7 \)

Add 15 to both sides:
\( 2x = 7 + 15 \)
\( 2x = 22 \)

Divide both sides by 2:
\( x = \frac{22}{2} \)
\( x = 11 \)

Answer:

\( x = 11 \)