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The worksheet in your image is focused on angle pairs formed by a transversal intersecting two parallel lines. Here's a breakdown of how to solve each part:

### Part A) **Name the relation between the angles formed by the transversal**:
The types of angle pairs involved are often classified as corresponding angles, alternate interior angles, alternate exterior angles, or vertical angles. Here are the likely answers:

1. **∠1 and ∠8**: These are **alternate exterior angles**.
2. **∠4 and ∠6**: These are **alternate interior angles**.
3. **∠2 and ∠6**: These are **corresponding angles**.
4. **∠3 and ∠5**: These are **alternate interior angles**.
5. **∠4 and ∠5**: These are **consecutive interior angles** (or same-side interior angles).
6. **∠1 and ∠5**: These are **corresponding angles**.
7. **∠2 and ∠7**: These are **alternate exterior angles**.

### Part B) **Finding the measures of the angles**:
This section shows four diagrams where you'll need to use your knowledge of supplementary, vertical, and corresponding angles.

1. **In the first diagram**:
   - Given: ∠X = 30°
   - Since ∠X and ∠Y are supplementary (they are on the same line), ∠Y = 180° − 30° = **150°**.

2. **In the second diagram**:
   - Given: ∠Y = 127°
   - ∠X and ∠Y are supplementary, so ∠X = 180° − 127° = **53°**.

3. **In the third diagram**:
   - Given: ∠X = 64°
   - ∠X and ∠Y are vertical angles, so ∠Y = **64°**.

4. **In the fourth diagram**:
   - Given: ∠Y = 73°
   - ∠X and ∠Y are supplementary, so ∠X = 180° − 73° = **107°**.

Would you like further details or clarification on any of these concepts?

### Related questions:
1. What are the properties of corresponding angles when a transversal cuts parallel lines?
2. How do alternate interior angles relate when lines are parallel?
3. What is the significance of supplementary angles in the context of a transversal?
4. Can you explain why vertical angles are always equal?
5. How can we use these angle relationships to prove lines are parallel?

**Tip**: For any transversal problem, always check if the lines are parallel. If they are, corresponding and alternate angles will have predictable relationships.

The worksheet in your image is focused on angle pairs formed by a transversal intersecting two parallel lines. Name the relations between the angles and find the measures of the specified angles.

Learn how to identify the relationships between angles formed by a transversal intersecting parallel lines. This includes corresponding angles, alternate interior and exterior angles, and supplementary angles. Step-by-step solutions included.

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