We are given that lines $a \parallel b$, and $\angle 8 = 125^\circ$. The diagram shows a transversal crossing parallel lines, forming multiple angles.

To solve for the remaining angles, we can apply the following principles:

1. Corresponding angles formed by a transversal with two parallel lines are equal.
2. Alternate interior angles are equal.
3. Same-side interior angles are supplementary (sum to $180^\circ$).

Let's calculate the measures of the angles step-by-step:

$\angle 8 = 125^\circ$ (Given)

1. $\angle 5$ (corresponding to $\angle 8$):
   $\angle 5 = \angle 8 = 125^\circ$

2. $\angle 7$ (supplementary to $\angle 8$):
   $\angle 7 = 180^\circ - \angle 8 = 180^\circ - 125^\circ = 55^\circ$

3. $\angle 6$ (corresponding to $\angle 7$):
   $\angle 6 = \angle 7 = 55^\circ$

4. $\angle 4$ (alternate interior angle to $\angle 8$):
   $\angle 4 = \angle 8 = 125^\circ$

5. $\angle 3$ (supplementary to $\angle 4$):
   $\angle 3 = 180^\circ - \angle 4 = 180^\circ - 125^\circ = 55^\circ$

6. $\angle 2$ (corresponding to $\angle 3$):
   $\angle 2 = \angle 3 = 55^\circ$

7. $\angle 1$ (alternate interior angle to $\angle 4$):
   $\angle 1 = \angle 4 = 125^\circ$

Summary of the angle measures:

• $\angle 1 = 125^\circ$
• $\angle 2 = 55^\circ$
• $\angle 3 = 55^\circ$
• $\angle 4 = 125^\circ$
• $\angle 5 = 125^\circ$
• $\angle 6 = 55^\circ$
• $\angle 7 = 55^\circ$

Would you like further details or clarifications on any of these steps?

Here are five related questions to deepen your understanding:

1. What are the conditions necessary for corresponding angles to be congruent?
2. How would the angle measures change if the parallel lines were not parallel?
3. What is the relationship between alternate interior angles and the parallel lines cut by a transversal?
4. How do you determine supplementary angles in a parallel lines and transversal situation?
5. Can you explain how to calculate the measures of angles formed by two non-parallel lines and a transversal?

Tip: When two parallel lines are cut by a transversal, always check if angles are alternate, corresponding, or same-side to find relationships easily!