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Find each angle measure. Answer questions 19 and 20

The image presents a pair of intersecting lines with the following angles labeled:

- Angle 1 (`∠1`)
- Angle 2 (`∠2`)
- A given angle of \( 123^\circ \)

### Solutions:

1. **Angle 1 (`m∠1`)**:
   - Angle 1 and the given angle of \( 123^\circ \) are vertical angles.
   - Vertical angles are always equal.
   - Therefore, \( m∠1 = 123^\circ \).

2. **Angle 2 (`m∠2`)**:
   - Angle 2 and the given angle of \( 123^\circ \) are on a straight line, making them supplementary angles.
   - Supplementary angles add up to \( 180^\circ \).
   - So, \( m∠2 + 123^\circ = 180^\circ \).
   - Solving for \( m∠2 \):
     \[
     m∠2 = 180^\circ - 123^\circ = 57^\circ
     \]

### Final Answers:
- \( m∠1 = 123^\circ \)
- \( m∠2 = 57^\circ \)

Would you like any further details or explanations on these concepts?

### Related Questions:
1. What are alternate interior angles, and how are they used in similar problems?
2. How would the values change if the given angle was \( 110^\circ \)?
3. Can you explain why vertical angles are always equal?
4. What is the difference between complementary and supplementary angles?
5. How do you calculate unknown angles when more than two lines intersect at a point?

### Tip:
Always remember that vertical angles are congruent, and adjacent angles on a straight line are supplementary!

Learn how to find each angle measure in a pair of intersecting lines with detailed step-by-step solutions. This problem covers key geometric concepts, including vertical angles and supplementary angles. Suitable for students in Grades 7-9.

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