Question

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

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 \(x + y=180^{\circ}\), if one angle is \(x^{\circ}\), its vertical angle is also \(x^{\circ}\), and the adjacent angle to \(x^{\circ}\) (on a straight - line) is \(y^{\circ}\).

Step2: Analyze each option

In option A, the angle relationships are consistent with vertical - angle and supplementary - angle properties. Vertical angles are equal (\(x^{\circ}\) angles are equal to each other and \(y^{\circ}\) angles are equal to each other), and adjacent angles on a straight - line are \(x^{\circ}\) and \(y^{\circ}\) which sum to 180°.

Answer:

A.