https://file.aiquickdraw.com/mathbot/file/1727411528885ox3kibby.jpg

In the image, you are asked to find the measures of two angles, \( \angle 1 \) and \( \angle 2 \), and justify the answer.

### Step-by-step solution:

1. **Identify given information**:
   - \( \angle 2 \) is marked as 78°.
   - The lines \( l \) and \( m \) appear to be parallel, as they are cut by the transversal \( t \).

2. **Determine \( m \angle 2 \)**:
   - From the diagram, \( m \angle 2 = 78^\circ \), since this angle is directly given.

3. **Find \( m \angle 1 \)**:
   - \( \angle 1 \) and \( \angle 2 \) are **alternate interior angles**, since they are on opposite sides of the transversal \( t \) and between the parallel lines \( l \) and \( m \).
   - By the **Alternate Interior Angles Theorem**, if two parallel lines are cut by a transversal, alternate interior angles are congruent.
   - Therefore, \( m \angle 1 = m \angle 2 \).
   - Hence, \( m \angle 1 = 78^\circ \).

### Conclusion:
- \( m \angle 1 = 78^\circ \)
- \( m \angle 2 = 78^\circ \)

Both are justified by the Alternate Interior Angles Theorem.

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Do you need more details on any part of the solution or have any specific questions? 

Here are five related questions to further expand your understanding:
1. What is the definition of alternate interior angles?
2. Can two non-parallel lines form congruent alternate interior angles?
3. What is the difference between corresponding angles and alternate interior angles?
4. How would the solution change if \( l \) and \( m \) were not parallel?
5. What is the Converse of the Alternate Interior Angles Theorem?

**Tip**: When working with parallel lines, always check the position of the transversal to identify congruent angles (like alternate interior or corresponding angles).

Find m∠1 and m∠2. Justify your answer.

Learn how to find the measures of two angles using the Alternate Interior Angles Theorem. The problem involves parallel lines cut by a transversal, and angle relationships are key to solving it. This problem is suitable for students in Grades 8-10.

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