To solve this problem, we will classify each pair of angles as either congruent (equal in measure) or supplementary (add up to 180°). We will also explain the reasoning based on angle relationships like corresponding angles, alternate interior angles, and others that occur when parallel lines are intersected by a transversal.

Given Information:

The image shows two parallel lines cut by a transversal, which creates multiple angles. These angles follow specific relationships depending on their positioning.

Solution:

1. a. ∠3 and ∠5:

   • Angle relationship: These are corresponding angles (same relative position at two intersections).
   • Conclusion: Congruent (Corresponding angles are always congruent).

2. b. ∠1 and ∠8:

   • Angle relationship: These are alternate exterior angles (opposite sides of the transversal and outside the parallel lines).
   • Conclusion: Congruent (Alternate exterior angles are congruent).

3. c. ∠2 and ∠6:

   • Angle relationship: These are corresponding angles.
   • Conclusion: Congruent (Corresponding angles are congruent).

4. d. ∠1 and ∠4:

   • Angle relationship: These are vertical angles (formed by intersecting lines and directly opposite each other).
   • Conclusion: Congruent (Vertical angles are congruent).

5. e. ∠4 and ∠5:

   • Angle relationship: These are consecutive interior angles (same side of the transversal and inside the parallel lines).
   • Conclusion: Supplementary (Consecutive interior angles sum up to 180°).

6. f. ∠3 and ∠7:

   • Angle relationship: These are alternate interior angles (opposite sides of the transversal and inside the parallel lines).
   • Conclusion: Congruent (Alternate interior angles are congruent).

7. g. ∠5 and ∠6:

   • Angle relationship: These are linear pair angles (adjacent angles that form a straight line).
   • Conclusion: Supplementary (Linear pair angles sum up to 180°).

8. h. ∠2 and ∠4:

   • Angle relationship: These are alternate interior angles.
   • Conclusion: Congruent (Alternate interior angles are congruent).

Would you like more detailed explanations or have any specific questions?

Related Questions:

1. What are the properties of alternate interior angles?
2. How do corresponding angles behave when lines are parallel?
3. Can you explain how a linear pair of angles is identified?
4. Why are consecutive interior angles supplementary?
5. How can you tell if two angles are congruent without knowing the specific measures?

Tip:

When identifying angle relationships, always look for the transversal and whether the angles are on the inside (interior) or outside (exterior) of the parallel lines to classify the angle pair type.