When two parallel lines are cut by a transversal, certain pairs of angles are always supplementary. Supplementary angles are two angles that add up to 180°. The pairs of angles that are always supplementary include:

1. Consecutive Interior Angles (or Same-Side Interior Angles): These are angles that are on the same side of the transversal and inside the parallel lines.

   • Example: If ∠3 and ∠5 are consecutive interior angles, then ∠3 + ∠5 = 180°.

2. Consecutive Exterior Angles (or Same-Side Exterior Angles): These are angles that are on the same side of the transversal but outside the parallel lines.

   • Example: If ∠1 and ∠7 are consecutive exterior angles, then ∠1 + ∠7 = 180°.

These angle relationships hold because parallel lines maintain a consistent distance, ensuring that these specific angle pairs sum to 180°.

Would you like more details or have any questions?

Here are 5 relative questions to expand on this concept:

1. What are alternate interior angles in this setup, and are they always congruent?
2. How do corresponding angles behave when two parallel lines are cut by a transversal?
3. Can you explain the difference between supplementary and complementary angles?
4. How can we prove that consecutive interior angles are supplementary?
5. What would happen to these angle relationships if the lines were not parallel?

Tip: Consecutive interior angles are a key indicator of whether two lines are parallel when cut by a transversal. If they are supplementary, the lines are parallel.