Let's solve the problems shown in the image by analyzing each statement and determining which lines are parallel using the appropriate theorems or postulates.

Here are the answers and justifications:

17. ∠2 is supplementary to ∠3.

• Justification: If two angles are supplementary (sum to 180°), and these are consecutive interior angles, then the lines cut by a transversal are parallel.
• Conclusion: The lines are parallel by the Consecutive Interior Angles Theorem.

18. ∠1 ≅ ∠3.

• Justification: If two corresponding angles are congruent, then the lines cut by a transversal are parallel.
• Conclusion: The lines are parallel by the Corresponding Angles Postulate.

19. ∠6 is supplementary to ∠7.

• Justification: As with question 17, if two consecutive interior angles are supplementary, the lines are parallel.
• Conclusion: The lines are parallel by the Consecutive Interior Angles Theorem.

20. ∠9 ≅ ∠12.

• Justification: If alternate interior angles are congruent, then the lines cut by the transversal are parallel.
• Conclusion: The lines are parallel by the Alternate Interior Angles Theorem.

21. m∠7 = 65°, m∠9 = 115°.

• Justification: These two angles are consecutive interior angles, and their sum is 180° (65° + 115° = 180°), meaning they are supplementary.
• Conclusion: The lines are parallel by the Consecutive Interior Angles Theorem.

22. ∠2 ≅ ∠10.

• Justification: These are corresponding angles. If corresponding angles are congruent, then the lines are parallel.
• Conclusion: The lines are parallel by the Corresponding Angles Postulate.

23. ∠1 ≅ ∠8.

• Justification: If alternate exterior angles are congruent, then the lines cut by a transversal are parallel.
• Conclusion: The lines are parallel by the Alternate Exterior Angles Theorem.

24. ∠8 ≅ ∠6.

• Justification: If corresponding angles are congruent, the lines are parallel.
• Conclusion: The lines are parallel by the Corresponding Angles Postulate.

25. ∠11 ≅ ∠7.

• Justification: These are alternate interior angles. If alternate interior angles are congruent, then the lines are parallel.
• Conclusion: The lines are parallel by the Alternate Interior Angles Theorem.

26. ∠5 ≅ ∠10.

• Justification: If corresponding angles are congruent, then the lines cut by a transversal are parallel.
• Conclusion: The lines are parallel by the Corresponding Angles Postulate.

Would you like more detailed explanations or have any specific questions?

Here are 5 related questions:

1. What is the difference between consecutive interior and alternate interior angles?
2. How do you identify corresponding angles when given a transversal?
3. Can two lines be parallel if their consecutive interior angles are not supplementary?
4. How does the Alternate Exterior Angles Theorem prove lines are parallel?
5. Why is it necessary for angles to be congruent or supplementary to prove lines are parallel?

Tip: When using a transversal to determine if lines are parallel, always check the type of angle relationship (corresponding, alternate interior, etc.) and apply the appropriate theorem.