1. **State the problem:** We have two parallel lines M and N cut by a transversal. We know the measure of an angle on line N is 75° and need to find the measure of angle $a$ on line M. 2. **Recall the rule:** When two parallel lines are cut by a transversal, corresponding angles are equal. 3. **Apply the rule:** Since lines M and N are parallel, the angle $a$ on line M corresponds to the 75° angle on line N. 4. **Conclusion:** Therefore, the measure of angle $a$ is equal to 75°. $$m\angle a = 75^\circ$$