Question

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

Explanation:

Step1: Recall parallel - line postulates

If two lines are cut by a transversal, then certain angle - relationships can prove the lines are parallel. One of the postulates states that if same - side interior angles are supplementary, then the two lines are parallel.

Step2: Analyze the given angles

In the case of two lines \(j\) and \(k\) cut by a transversal, \(\angle3\) and \(\angle4\) are same - side interior angles. If \(\angle3\) and \(\angle4\) are supplementary, i.e., \(\angle3+\angle4 = 180^{\circ}\), then by the same - side interior angles postulate, \(j\parallel k\).

Answer:

\(\angle3\) and \(\angle4\) are supplementary