https://file.aiquickdraw.com/mathbot/file/1730733583506inx8cvj7.jpg

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.

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### 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°.

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

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### 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?

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

Given various angle measures with parallel lines and transversals, find the unknown angles using angle relationships.

Learn how to find missing angle measures in a set of parallel lines and transversals using angle relationships. This solution explores concepts like corresponding, alternate interior, and alternate exterior angles with step-by-step reasoning, perfect for Grades 8-10.

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