Let’s go through the problems step by step. I'll provide answers along with explanations based on the properties of parallel lines and angle relationships.

Solutions

5. If the measure of ∠1 = 160°, then the measure of ∠5 = ?

• Explanation: ∠1 and ∠5 are corresponding angles because they are on the same side of the transversal and in corresponding positions. Corresponding angles are congruent when the lines are parallel.
• Answer: ∠5 = 160°.

6. If the measure of ∠6 = 37°, then the measure of ∠4 = ?

• Explanation: ∠6 and ∠4 are alternate interior angles, which are also congruent when the lines are parallel.
• Answer: ∠4 = 37°.

7. If the measure of ∠8 = 82°, then the measure of ∠3 = ?

• Explanation: ∠8 and ∠3 are alternate exterior angles. Since the lines are parallel, alternate exterior angles are congruent.
• Answer: ∠3 = 82°.

8. If the measure of ∠4 = 60°, then the measure of ∠5 = ?

• Explanation: ∠4 and ∠5 are consecutive interior angles (same side of the transversal), and their measures add up to 180° because they form a supplementary pair.
• Calculation: ∠5 = 180° - 60° = 120°.
• Answer: ∠5 = 120°.

9. Your friend finds the measure of ∠6. Is your friend correct? Explain your reasoning.

• The figure shows that ∠6 and the 103° angle are alternate exterior angles. Since the lines are parallel, alternate exterior angles are congruent.
• Conclusion: Your friend is correct; ∠6 = 103°.

Would you like further explanations for any of these steps, or do you have any additional questions?

Related Questions

1. If the measure of ∠2 is 41°, what is the measure of ∠6?
2. Given ∠3 = 41°, find the measure of ∠7.
3. If ∠7 = 75°, what is the measure of ∠2?
4. Determine the measure of ∠8 if ∠1 is 117°.
5. If ∠5 = 125°, what is the measure of ∠4?

Tip

Remember, when dealing with parallel lines, corresponding angles and alternate interior/exterior angles are congruent, while consecutive interior angles add up to 180°.