This problem involves a set of parallel lines cut by a transversal. Given that ∠4 = 135°, we can use the properties of angles formed by parallel lines and a transversal to find ∠7 and ∠8.

Step-by-step solution:

1. Alternate Interior Angles: Since the lines are parallel, ∠4 and ∠8 are alternate interior angles. Therefore, their measures are equal: $\text{m}∠4 = \text{m}∠8 = 135°$

2. Linear Pair: Angles ∠7 and ∠8 form a linear pair, meaning they are supplementary. The sum of these two angles must equal 180°. Thus, we can calculate m∠7 as follows: $\text{m}∠7 = 180° - \text{m}∠8 = 180° - 135° = 45°$

Final Answer:

• m∠7 = 45°
• m∠8 = 135°

Would you like more details or have any other questions?

Here are some related questions you might find useful:

1. How do alternate interior angles help in solving transversal problems?
2. What are linear pairs, and how do they relate to supplementary angles?
3. Can you explain the difference between corresponding angles and alternate interior angles?
4. What is the relationship between the sum of angles on a straight line?
5. How do you identify vertical angles in such diagrams?

Tip: Always remember that parallel lines cut by a transversal produce congruent alternate interior and corresponding angles!