Question

given ( m parallel n ), find the value of ( x ).

Explanation:

Step1: Identify angle relationship

Since \( m \parallel n \), the two angles \( (3x - 15)^\circ \) and \( (x + 7)^\circ \) are alternate interior angles, so they are equal.
\[ 3x - 15 = x + 7 \]

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:

\( x = 11 \)