1. **State the problem:** Given two parallel lines $a$ and $b$ cut by a transversal, determine the relationship between $m \angle 1$ and $m \angle 8$. 2. **Recall the angle relationships with parallel lines:** When two parallel lines are cut by a transversal, several angle pairs are congruent: - Corresponding angles are equal. - Alternate interior angles are equal. - Alternate exterior angles are equal. - Same-side interior angles are supplementary. 3. **Identify angles 1 and 8:** Angles 1 and 8 lie in corresponding positions relative to the two parallel lines and the transversal. 4. **Conclusion:** Since $a \parallel b$, $m \angle 1 = m \angle 8$ because they are corresponding angles. **Final answer:** $m \angle 1 = m \angle 8$ because they are corresponding angles.