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The worksheet you're working on is about angles formed by parallel lines and transversals. Let's go through the first few problems and solve them.

**Key Concept**: 
When two parallel lines are intersected by a transversal, several types of angle pairs are formed, such as:
- **Corresponding angles**: These are equal.
- **Alternate interior angles**: These are equal.
- **Alternate exterior angles**: These are equal.
- **Consecutive interior angles** (or co-interior angles): These sum up to \(180^\circ\).

### Solutions:

1. **Problem 1**:
   The given angle is \(101^\circ\). The angle indicated is on a straight line with this, so they form a **linear pair**, meaning their sum is \(180^\circ\).
   - The measure of the missing angle is \(180^\circ - 101^\circ = 79^\circ\).

2. **Problem 2**:
   The given angle is \(80^\circ\). The missing angle is vertically opposite, so it is equal to \(80^\circ\) because **vertical angles** are congruent.
   - The measure of the missing angle is \(80^\circ\).

3. **Problem 3**:
   The given angle is \(122^\circ\). The missing angle is on the opposite side of the transversal, which means they form a **linear pair**. Their sum is \(180^\circ\).
   - The measure of the missing angle is \(180^\circ - 122^\circ = 58^\circ\).

4. **Problem 4**:
   The given angle is \(53^\circ\). The missing angle is an **alternate interior angle**, so it is equal to \(53^\circ\).
   - The measure of the missing angle is \(53^\circ\).

5. **Problem 5**:
   The given angle is \(114^\circ\). The missing angle is on the opposite side of the transversal, and they form a **linear pair**. Their sum is \(180^\circ\).
   - The measure of the missing angle is \(180^\circ - 114^\circ = 66^\circ\).

6. **Problem 6**:
   The given angle is \(89^\circ\). The missing angle is vertically opposite, so it is equal to \(89^\circ\).
   - The measure of the missing angle is \(89^\circ\).

Do you want detailed explanations for any specific problem or further assistance? Let me know!

Here are 5 questions to further practice:
1. What is the relationship between alternate exterior angles?
2. How do you identify corresponding angles on parallel lines?
3. Why do consecutive interior angles always sum up to \(180^\circ\)?
4. What is the difference between vertical and adjacent angles?
5. If two parallel lines are intersected by two transversals, how many pairs of corresponding angles are formed?

**Tip**: Always look for angle relationships (like alternate interior or corresponding angles) when parallel lines are involved, as it simplifies solving for unknown angles.

Find the measure of each angle indicated in the diagram involving parallel lines and transversals.

This guide explains how to solve for unknown angles when parallel lines are intersected by a transversal. Key concepts include corresponding angles, alternate interior angles, and vertical angles. Learn step-by-step solutions with examples suitable for Grades 8-10.

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