If lines \( m \) and \( n \) are parallel and one angle (let's say angle 1) is \( 135^\circ \), then we can determine the corresponding angle (angle 8) based on the properties of parallel lines and transversals.
Assuming angle 1 is situated such that it is an interior angle created by a transversal intersecting lines \( m \) and \( n \), the corresponding angle to angle 1 on the opposite side of the transversal (angle 8) will be equal to angle 1.
Since angle 1 is \( 135^\circ \):
\[ \text{Measure of angle 8} = 135^\circ \]
If angle 8 is an alternate interior angle, it follows the same logic, and thus:
\[ \text{Measure of angle 8} = 135^\circ \]
So, the measure of angle 8 is also \( 135^\circ \).