https://file.aiquickdraw.com/mathbot/file/1727092923115n640qumx.jpg

Looking at the diagram, we can see that two lines are cut by a transversal, and angles 1 and 2 are formed. Angle 2 is given as \( 49^\circ \), and you are asked to find \( \angle 1 \).

### Identifying the Angle Relationship:
- Lines \( l \) and \( m \) appear to be parallel, and the transversal \( t \) crosses them.
- Angles 1 and 2 are on opposite sides of the transversal but inside the parallel lines, making them **alternate interior angles**.

### Conclusion:
By the **Alternate Interior Angles Theorem**, \( \angle 1 = \angle 2 \). Since \( \angle 2 = 49^\circ \), \( \angle 1 = 49^\circ \).

### Justification:
The answer is \( m\angle 1 = 49^\circ \) by the **Alternate Interior Angles Theorem**.

Would you like any further clarification or details on this?

Here are 5 follow-up questions to deepen your understanding:
1. What are the properties of alternate exterior angles?
2. How can you prove that two lines are parallel using corresponding angles?
3. What is the difference between same-side interior angles and alternate interior angles?
4. Can vertical angles ever be supplementary?
5. In what situations are same-side interior angles supplementary?

**Tip:** Always verify if two lines are parallel before applying angle theorems related to transversals.

Find the measure of angle 1 (m∠1) and angle 2 (m∠2). Justify your answer based on the image provided, where lines l and m are cut by transversal t, and m∠2 = 49°.

Learn how to find the measure of angle 1 when lines are cut by a transversal. This problem uses the Alternate Interior Angles Theorem and is suitable for students in Grades 9-10.

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