Question

select the correct answer.
lines \\(\vec{wx}\\) and \\(\vec{yz}\\) above are parallel. what is the relationship between \\(\angle 1\\) and \\(\angle 5\\)?
image of two parallel lines (\\(\vec{wx}\\) and \\(\vec{yz}\\)) cut by a transversal, with angles labeled 1, 2, 3, 4 (around \\(\vec{wx}\\)) and 5, 6, 7, 8 (around \\(\vec{yz}\\))
\\(\bigcirc\\) a. congruent, because they are alternate external angles.
\\(\bigcirc\\) b. congruent, because they are corresponding angles.
\\(\bigcirc\\) c. supplementary, because they are corresponding angles.
\\(\bigcirc\\) d. supplementary, because they are alternate interior angles.

Explanation:

Step1: Recall Corresponding Angles

When two parallel lines are cut by a transversal, corresponding angles are congruent. Corresponding angles are in the same relative position at each intersection.

Step2: Identify ∠1 and ∠5

∠1 and ∠5 are in the same relative position (top - left) at their respective intersections of the transversal with the parallel lines \( \overleftrightarrow{WX} \) and \( \overleftrightarrow{YZ} \). So they are corresponding angles, hence congruent.

Step3: Eliminate Other Options

• Option A: Alternate external angles are different from this case.
• Option C: Corresponding angles are congruent, not supplementary.
• Option D: Alternate interior angles are also congruent but ∠1 and ∠5 are not alternate interior angles.

Answer:

B. Congruent, because they are corresponding angles.