Question

given m || n, find the value of x.

Explanation:

Step1: Identify alternate interior angles

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

Step2: Solve for \( x \)

Subtract \( x \) from both sides:
\[
7 = 2x - 15
\]
Add 15 to both sides:
\[
22 = 2x
\]
Divide by 2:
\[
x = 11
\]

Answer:

\( 11 \)