In the diagram below, lines x and y are parallel and cut by a transversal, and m∠1 = 53°.
 


Which argument explains why m∠3 is also 53°?

Since lines \( x \) and \( y \) are parallel and cut by a transversal, the angles formed by the transversal exhibit specific relationships. 

In this case, \( \angle 1 \) and \( \angle 3 \) are **corresponding angles**. When a transversal cuts two parallel lines, corresponding angles are congruent, meaning they have the same measure.

Thus, the argument is that **\( \angle 1 \) and \( \angle 3 \) are corresponding angles**, and therefore, \( m\angle 3 = 53^\circ \).

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Here are 5 questions related to this concept:
1. What are alternate interior angles, and how are they related in parallel lines?
2. How can we prove that corresponding angles are congruent using axioms?
3. Can the transversal create supplementary angles? If so, which ones?
4. What are alternate exterior angles, and how do they relate to parallel lines?
5. How would the relationships change if the lines weren't parallel?

**Tip:** When dealing with parallel lines and transversals, look for angle pairs like corresponding, alternate interior, and alternate exterior to identify equal angles.

In the diagram below, lines x and y are parallel and cut by a transversal, and m∠1 = 53°. Which argument explains why m∠3 is also 53°?

Understand why corresponding angles formed by a transversal cutting through parallel lines are congruent. This problem demonstrates how m∠1 equals m∠3, both measuring 53°. Ideal for students in Grades 7-9 learning about angle relationships and parallel lines.

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