https://file.aiquickdraw.com/mathbot/file/1727309795704jsjqk48k.jpg

In the given image, we need to find the measures of ∠1 and ∠2 and justify each answer. Let's analyze the situation:

### Given:
- ∠2 is 75°, as shown in the diagram.
- The two lines labeled \(\ell\) and \(m\) are parallel, with the transversal \(t\) crossing them, forming angles 1 and 2.

### Step-by-step Analysis:

1. **Relationship between ∠1 and ∠2:**
   ∠1 and ∠2 are **corresponding angles** because they are formed by the transversal \(t\) crossing the two parallel lines \(\ell\) and \(m\). Corresponding angles are congruent when two parallel lines are cut by a transversal.

   Therefore:
   \[
   m\angle1 = m\angle2 = 75^\circ
   \]

### Conclusion:
- **m∠1 = 75°**, because corresponding angles are equal when two parallel lines are intersected by a transversal.
- **m∠2 = 75°**, given in the diagram.

Let me know if you need more details or clarifications!

### Further Questions:
1. What are alternate interior angles and how are they related when lines are parallel?
2. How would the result change if the lines were not parallel?
3. What other angle pairs can be identified in this diagram?
4. Can you identify vertical angles in this diagram, and what is their property?
5. What is the sum of the angles at a point where the transversal crosses one of the parallel lines?

**Tip:** Always remember that corresponding angles are congruent when a transversal crosses two parallel lines!

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

Solve for the measures of ∠1 and ∠2, where ∠2 is given as 75°. Using the corresponding angles theorem, learn why ∠1 also equals 75° when a transversal intersects two parallel lines. Suitable for students in Grades 8-10.

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