Question

in the diagram shown, if x + y = 180, label the remaining angle measures as x° or y°. choose the correct answer below.

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal, vertical angles are equal, and adjacent angles on a straight - line are supplementary (sum to 180°). Given \(x + y=180\), if we have a pair of parallel lines cut by a transversal, the angle that is vertical to \(x\) is \(x\), and the angle that is vertical to \(y\) is \(y\). Also, the angle adjacent to \(x\) (on the same side of the transversal and between the parallel lines) is \(y\), and the angle adjacent to \(y\) (on the same side of the transversal and between the parallel lines) is \(x\).

Step2: Analyze each option

In option A, the angle - labeling follows the rules of vertical angles and supplementary adjacent angles formed by two parallel lines cut by a transversal. The vertical angles are equal (\(x\) with \(x\) and \(y\) with \(y\)), and the adjacent angles on the straight - line formed by the transversal and the parallel lines are supplementary (\(x + y = 180\)).

Answer:

A.