Given that angle 1 is 135° and the lines M and N are parallel, we can apply the properties of angles formed by a transversal cutting through parallel lines.
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Identify Angles:
- Since angle 1 is 135°, and it is an exterior angle relative to the angles formed at the intersections, we can determine the corresponding interior angle created on line M which is adjacent to angle 1. Specifically,
- Angle 2 (the corresponding angle on line M) would be supplementary to angle 1. Thus, angle 2 = 180° - 135° = 45°.
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Find Angle 6 and its Relation to Angle 2:
- Angle 6 is vertical to angle 2, so angle 6 = angle 2 = 45°.
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Find Angle 8:
- Since M and N are parallel lines, angle 8 (located on line N corresponding to angle 2) is equal to angle 2 due to corresponding angles.
- Therefore, angle 8 = angle 2 = 45°.
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Calculate the Sum of Angles 6 and 8:
- The sum of angle 6 and angle 8 is: \[ \text{Angle 6} + \text{Angle 8} = 45° + 45° = 90° \]
Thus, the sum of angle 6 and angle 8 is \( \boxed{90°} \).