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I see that you've uploaded an image of a worksheet related to angles formed by parallel lines and transversals. The task is to identify the type of angle pair and then use that information to solve for the unknown angles.

Here’s a breakdown of how to approach each problem based on what I can see:

1. **Type of angle pair**: The angles formed by parallel lines and a transversal are often **corresponding**, **alternate interior**, **alternate exterior**, or **consecutive interior** (same-side interior) angles.
   
2. **Using properties of angle pairs**:
   - **Corresponding angles** are equal.
   - **Alternate interior and alternate exterior angles** are equal.
   - **Consecutive interior angles** (also known as co-interior) sum to 180°.

I’ll now provide explanations for a few problems from the worksheet.

### 1. **Problem 1**
- **Type of angle pair**: These angles seem to be *corresponding angles*.
- **Angle relationship**: Corresponding angles are equal.
- If one of the angles is 108°, the other is also 108°.
- \( x = 108^\circ \).

### 2. **Problem 2**
- **Type of angle pair**: These angles are *consecutive interior angles* (same side of the transversal).
- **Angle relationship**: Consecutive interior angles sum to 180°.
- Given one angle is 138°, the other angle is \( 180^\circ - 138^\circ = 42^\circ \).
- \( x = 42^\circ \).

### 3. **Problem 3**
- **Type of angle pair**: These are *vertical angles*.
- **Angle relationship**: Vertical angles are equal.
- So, if one angle is \( 102^\circ \), the other must also be \( 102^\circ \).
- \( x = 102^\circ \).

### 4. **Problem 4**
- **Type of angle pair**: These are *corresponding angles*.
- **Angle relationship**: Corresponding angles are equal.
- If one angle is \( 101^\circ \), then the other angle is also \( 101^\circ \).
- \( x = 101^\circ \).

Would you like a detailed breakdown for the remaining problems or have any further questions?

Here are five relative questions that build on this:

1. What are the properties of alternate interior angles when parallel lines are cut by a transversal?
2. How do you identify consecutive interior angles in a diagram involving parallel lines?
3. Can vertical angles ever be unequal? Why or why not?
4. What is the sum of consecutive interior angles, and how does it help in solving unknown angles?
5. How can corresponding angles be used to verify whether two lines are parallel?

**Tip**: When identifying angle pairs, always look for whether they are on opposite or the same side of the transversal. This can help determine whether they are alternate or corresponding angles.

Identify the type of angle pair and solve for the unknown angle in each diagram involving parallel lines cut by a transversal.

Learn how to solve for unknown angles by identifying angle pairs in parallel lines cut by a transversal. This worksheet covers corresponding, alternate, and consecutive interior angles, as well as vertical angles, suitable for students in Grades 7-9.

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