1. **State the problem:** We are given two lines, a and b, cut by a transversal, creating angles numbered 1 through 8. We know $m\angle 3 = 105^\circ$ and $m\angle 6 = 75^\circ$. We need to determine which statements about the parallelism of lines a and b are true. 2. **Recall angle relationships when lines are parallel:** - Consecutive interior angles are supplementary (sum to $180^\circ$). - Corresponding angles are congruent (equal in measure). - Alternate interior angles are congruent. 3. **Check if lines a and b are parallel using consecutive interior angles:** Consecutive interior angles here are $\angle 3$ and $\angle 6$. Calculate their sum: $$m\angle 3 + m\angle 6 = 105^\circ + 75^\circ = 180^\circ$$ Since the sum is $180^\circ$, consecutive interior angles are supplementary. 4. **Check if corresponding angles are congruent:** Corresponding angles would be pairs like $\angle 3$ and $\angle 7$ or $\angle 2$ and $\angle 6$. We only know $m\angle 3$ and $m\angle 6$, which are not corresponding angles. Since $m\angle 3 \neq m\angle 6$, corresponding angles are not congruent. 5. **Check if alternate interior angles are congruent:** Alternate interior angles are pairs like $\angle 3$ and $\angle 5$, or $\angle 4$ and $\angle 6$. We don't have $m\angle 5$ or $m\angle 4$, so we cannot confirm congruence. But since $m\angle 3 \neq m\angle 6$, and these are not alternate interior pairs, this does not apply. 6. **Conclusion:** - The statement "Line a is parallel to line b because consecutive interior angles are supplementary" is true. - The statements about corresponding angles and alternate interior angles being congruent are false based on given data. - Therefore, line a is parallel to line b. **Final answer:** Line a is parallel to line b because consecutive interior angles are supplementary.