To solve the problem involving angles formed by parallel lines M and N, we need to utilize the properties of angles formed by a transversal intersecting parallel lines.
Given that angle 1 is \(135^\circ\) and lines M and N are parallel, we can identify the positions of angles 6 and 8 with respect to angle 1.
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Identifying Corresponding Angles:
- If we assume that angles are numbered such that angle 1 and angle 6 are corresponding angles, then angle 6 must also measure \(135^\circ\) (because corresponding angles are congruent).
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Finding angle 8:
- Angle 8 might be an alternate interior angle with angle 1. In this case, angle 8 will measure \(180^\circ - 135^\circ = 45^\circ\) (since alternate interior angles are equal, angle 8 would also be exactly opposite angle 1).
Now we can find the sum of angle 6 and angle 8:
\[ \text{Sum} = \text{Angle 6} + \text{Angle 8} = 135^\circ + 45^\circ = 180^\circ \]
Therefore, the sum of angle 6 and angle 8 is \(180^\circ\).
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