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.