To determine the measure of angle 8, we need more context about the relationships between angles 1 and 8 and how they are formed in relation to the parallel lines M and N.
Assuming angle 1 (135°) is an exterior angle formed by a transversal crossing the parallel lines M and N, then angle 8 could be an interior angle on the same side of the transversal.
In this case, when two parallel lines are cut by a transversal, the following properties hold:
- Corresponding angles are equal.
- Alternate interior angles are equal.
- Consecutive interior angles are supplementary.
If angle 1 is 135° (an exterior angle), we can find angle 8, which may be the interior angle on the same side of the transversal, by noting that they are supplementary (they form a linear pair). Thus, we have:
\[ \text{angle 1} + \text{angle 8} = 180° \]
Substituting the given value:
\[ 135° + \text{angle 8} = 180° \]
To find angle 8:
\[ \text{angle 8} = 180° - 135° \] \[ \text{angle 8} = 45° \]
So, if angle 8 is indeed the interior angle on the same side of the transversal as angle 1, then angle 8 measures 45°.
If the relationship between angle 1 and angle 8 is different, please provide additional details to give a precise answer.