Question

Given a∥b, and c is not parallel to a or b, which statements must be true?

1) m∠1=m∠8 (the measure of angle 1 equals the measure of angle 8)
2) m∠5=m∠9 (the measure of angle 5 equals the measure of angle 9)
3) m∠1=m∠12 (the measure of angle 1 equals the measure of angle 12)
4) m∠3=m∠7 (the measure of angle 3 equals the measure of angle 7)

Answer 1

Without a specific diagram, it's challenging to say which angle relationships hold true. However, corresponding angles and alternate angles (interior and exterior) are equal when lines are cut by a transversal, which may help in determining the truth of the statements about angles formed by parallel lines a and b, and the non-parallel line c.

Step-by-step explanation:

Given that line a is parallel to line b, and line c is not parallel to either line a or line b, we need to determine which statements regarding angles formed by these lines must be true. Without a diagram, we cannot say for certain which angles are being referred to specifically as m°1, m°8, etc. However, we can discuss typical angle relationships in parallel lines cut by a transversal:

• Corresponding angles are equal.
• Alternate interior angles are equal.
• Alternate exterior angles are equal.
• Consecutive interior angles (or same side interior angles) are supplementary.

If angle 1 and angle 8 are corresponding or alternate exterior angles, then statement 1 would be true. If angle 5 and angle 9 are corresponding or alternate interior angles, statement 2 would be correct. Similarly for statements 3 and 4, we need more context from a diagram or further explanation of the angle positions.