https://file.aiquickdraw.com/mathbot/file/1726762078134hytxami6.jpg

The image presents a transversal \( m \) intersecting two parallel lines \( v \) and \( w \), forming angles labeled as \( 1 \), \( 2 \), and \( 3 \). The student's claims are:

1. Angles \( 2 \) and \( 3 \) are corresponding angles, so they are congruent.
2. Angles \( 2 \) and \( 1 \) are a linear pair, so they are supplementary.

The question asks which is the best conclusion based on these claims.

### Analysis:
- Since \( 2 \) and \( 3 \) are corresponding angles formed by the transversal \( m \) and parallel lines \( v \) and \( w \), they are congruent. Thus, \( \angle 2 = \angle 3 \).
- Angles \( 2 \) and \( 1 \) are a linear pair, meaning they are adjacent and supplementary. This implies \( \angle 2 + \angle 1 = 180^\circ \).

Given this information, we can determine that the sum of \( \angle 1 + \angle 2 + \angle 3 \) must equal \( 180^\circ \) because \( \angle 2 = \angle 3 \) and \( \angle 2 + \angle 1 = 180^\circ \).

### Conclusion:
The best answer is:
- **The measures of angles 1, 2, and 3 sum to 180°**.

This corresponds to the last option.

### Do you have any questions or would you like more details?

Here are 5 related questions you might explore:
1. What is the definition of corresponding angles?
2. How can we prove that corresponding angles are congruent when a transversal crosses parallel lines?
3. What is a linear pair, and how do we know they are supplementary?
4. How does the sum of the interior angles of a triangle relate to this situation?
5. Can two angles be congruent and supplementary at the same time?

**Tip:** Remember that a transversal cutting across parallel lines always creates pairs of corresponding and alternate angles that have specific relationships.

Transversal m intersects parallel lines v and w, forming angles labeled as 1, 2, and 3. A student claims that angles 2 and 3 are corresponding angles, so they are congruent, and angles 2 and 1 are a linear pair, so they are supplementary. What is the best conclusion based on these claims?

Explore the properties of a transversal intersecting parallel lines. Learn how corresponding angles are congruent and linear pairs are supplementary. This problem is suitable for students in Grades 8-10, focusing on key geometry concepts such as corresponding angles and the linear pair postulate.

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