Question

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

Explanation:

Step1: Identify the relationship (alternate interior angles)

Since \( m \parallel n \), the angles \( (8x - 9)^\circ \) and \( (6x + 1)^\circ \) are alternate interior angles, so they are equal.
\[
8x - 9 = 6x + 1
\]

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides:
\[
8x - 6x - 9 = 1
\]
\[
2x - 9 = 1
\]
Add 9 to both sides:
\[
2x = 1 + 9
\]
\[
2x = 10
\]
Divide both sides by 2:
\[
x = \frac{10}{2}
\]
\[
x = 5
\]

Answer:

\( x = 5 \)