If M

To address your questions based on the angles formed by parallel lines cut by a transversal, let's go step by step.

1. **Angle 2**: If angle 1 is 135°, and M and N are parallel lines, then angle 2 is the corresponding angle to angle 1 on the transversal. Therefore, angle 2 is also **135°**.

2. **Angle 8**: If angles M and N are parallel and angle 1 is 135°, then angle 8 is the alternate interior angle relative to angle 1. Thus, angle 8 is **45°** (since 180° - 135° = 45°).

3. **Angle 7**: Again, with M and N as parallel lines, angle 7 would be the same as angle 2, since they are corresponding angles. Therefore, angle 7 is **135°**.

4. **Sum of angle 6 and angle 8**: To find the sum of angle 6 and angle 8, we know that angle 8 is 45° as calculated above. Since angle 6 is the same as angle 1 in this case, angle 6 is 135°. Therefore, the sum is 135° + 45° = **180°**.

5. **Angle 3 when angle 1 is 63°**: If angle 1 is 63°, then angle 3, which is a vertical angle to angle 1, would also measure **63°**, because vertical angles are equal.

Thus, the correct choice for angle 3 would be: "Angle 3 is 63° because angle 1 and angle 3 are vertical angles."