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