Question

Proof: It is given that ∠x and ∠y are supplementary. ∠z and ∠w are also supplementary, so since ______ are corresponding angles, a || b. And ∠t and ∠u, ∠v and ∠s.

A) ∠x ∠w
B) ∠x ∠t
C) ∠y ∠u
D) ∠y ∠v

Answer 1

The proof involves corresponding angles and parallel lines. ∠x and ∠w are corresponding angles, so a || b.

Step-by-step explanation:

The given proof involves the concept of corresponding angles and parallel lines. Since ∠x and ∠y are supplementary and ∠z and ∠w are supplementary, we can conclude that ∠x and ∠w are corresponding angles.

Since the corresponding angles of a transversal intersecting two parallel lines are congruent, this implies that line a is parallel to line b. Therefore, the correct choice is option A) ∠x ∠w.

Answer 2

Based on the given information, the corresponding angles ∠x and ∠w are supplementary, which implies that lines a and b are parallel.

Step-by-step explanation:

In this question, we are given that angle x and angle y are supplementary, and angle z and angle w are supplementary. According to the corresponding angles postulate, if two parallel lines are intersected by a transversal, then the corresponding angles are congruent. Since the angles x and w are corresponding angles and they are supplementary, we can conclude that a || b (lines a and b are parallel).

From the given information, we cannot determine the relationship between angle x and angle t, or angle y and angle u. Therefore, neither option B) ∠x ∠t nor option C) ∠y ∠u can be proven based on the given information. The correct answer is option A) ∠x ∠w because they are corresponding angles and supplementary.