Question

∠2≅∠3 ∠4 and ∠5 are supplementary ∠1 and ∠3 are supplementary ∠2≅∠5 which of the following would prove that j is parallel to k?

Explanation:

Step1: Recall parallel - line postulates

When two lines are cut by a transversal, if corresponding angles are congruent, the lines are parallel. If alternate - interior angles are congruent, the lines are parallel. If same - side interior angles are supplementary, the lines are parallel.

Step2: Analyze each option

• $\angle2\cong\angle3$: These are vertical angles. Vertical angles being congruent does not prove lines parallel.
• $\angle4$ and $\angle5$ are supplementary: These are same - side interior angles. If same - side interior angles formed by a transversal cutting two lines are supplementary, then the two lines are parallel.
• $\angle1$ and $\angle3$ are supplementary: These are not angles that can be used to prove the parallelism of $j$ and $k$ based on standard parallel - line postulates.
• $\angle2\cong\angle5$: These are not corresponding, alternate - interior, or angles with a relationship that directly proves parallel lines.

Answer:

$\angle4$ and $\angle5$ are supplementary