Given that angle 1 is 135° and the lines M and N are parallel, we can analyze the relationships between the angles formed by the transversal.
Angle 1 is an exterior angle on the top side of the transversal. The angle directly opposite angle 1 (angle 5) is also 135° since they are vertical angles and are equal.
Since angles on a straight line sum to 180°, we can find angle 2:
\[ \text{Angle 2} = 180° - \text{Angle 1} = 180° - 135° = 45° \]
Now, looking at angle 2 and angle 6 which are corresponding angles (because they are in the same position relative to the parallel lines and the transversal), we can say:
\[ \text{Angle 6} = \text{Angle 2} = 45° \]
Next, angle 6 is supplementary to angle 8 (because they are on the same line created by the transversal where angle 8 is located). Therefore, we find angle 8 as follows:
\[ \text{Angle 8} = 180° - \text{Angle 6} = 180° - 45° = 135° \]
Now we can find the sum of angle 6 and angle 8:
\[ \text{Sum of angle 6 and angle 8} = \text{Angle 6} + \text{Angle 8} = 45° + 135° = 180° \]
Thus, the sum of angle 6 and angle 8 is:
\[ \boxed{180°} \]