Since lines \( m \) and \( n \) are parallel and \( \angle 1 \) and \( \angle 8 \) are alternate exterior angles, they must be equal. Therefore, we can set up the equation:
\[ m\angle 1 = m\angle 8 \]
Substituting the values we have:
\[ 9x - 12 = 105 \]
Now, solve for \( x \):
- Add 12 to both sides:
\[ 9x = 105 + 12 \] \[ 9x = 117 \]
- Now, divide both sides by 9:
\[ x = \frac{117}{9} \] \[ x = 13 \]
Thus, the value of \( x \) is \( 13 \).
The correct response is:
13