https://file.aiquickdraw.com/mathbot/file/17268324541782tjqre6c.jpg

Let's go over the image and solve the questions one by one:

1. **Question 15: Same-Side Interior Angles**
   - Same-side interior angles lie on the same side of the transversal and between the two parallel lines.
   - The pair of same-side interior angles in the diagram is \( \angle 3 \) and \( \angle 5 \), and \( \angle 4 \) and \( \angle 6 \).

2. **Question 16: Corresponding Angles**
   - Corresponding angles are those in matching corners when two lines are crossed by a transversal.
   - The pairs of corresponding angles are: \( \angle 1 \) and \( \angle 5 \), \( \angle 2 \) and \( \angle 6 \), \( \angle 3 \) and \( \angle 7 \), and \( \angle 4 \) and \( \angle 8 \).

3. **Question 17: Alternate Exterior Angles**
   - Alternate exterior angles are on opposite sides of the transversal and outside the two lines.
   - The pairs of alternate exterior angles are: \( \angle 1 \) and \( \angle 7 \), and \( \angle 2 \) and \( \angle 8 \).

4. **Question 18: Which Angles are Supplementary and Congruent to \( \angle 1 \)?**
   - **Supplementary to \( \angle 1 \):** Supplementary angles add up to \( 180^\circ \).
     - \( \angle 1 \) and \( \angle 2 \) are supplementary.
   - **Congruent to \( \angle 1 \):** Congruent angles are equal in measure.
     - \( \angle 1 \) is congruent to \( \angle 4 \), \( \angle 5 \), and \( \angle 8 \).

5. **Questions 19 and 20: Find Each Angle Measure**
   - **Given: \( m\angle 2 = 123^\circ \)**
   - **Find \( m\angle 1 \):** Since \( \angle 1 \) and \( \angle 2 \) are supplementary, they add up to \( 180^\circ \).
     \[
     m\angle 1 = 180^\circ - 123^\circ = 57^\circ
     \]
   - Therefore, \( m\angle 1 = 57^\circ \).
   
   - **\( m\angle 2 \) is already given as \( 123^\circ \)**.

Would you like a detailed explanation on any of these topics? Here are 5 related questions:

1. How do you determine which angles are congruent in a transversal setup?
2. What is the significance of alternate interior angles?
3. How do corresponding angles help in proving lines are parallel?
4. Can you explain why some angles are supplementary when two lines are cut by a transversal?
5. How would you calculate the angle measures if the parallel lines are not horizontal?

**Tip:** When working with parallel lines and a transversal, always look for patterns like "Z" shapes (alternate interior angles) and "F" shapes (corresponding angles).

Identify a pair of angles for each type: same-side interior, corresponding, alternate exterior. Find the measures of angles given in the diagram.

Explore how to identify same-side interior, corresponding, and alternate exterior angles in parallel lines crossed by a transversal. Learn to calculate angle measures effectively with clear diagrams and examples. This guide is ideal for students in Grades 8 to 10 studying geometry.

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