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 \(x + y=180^{\circ}\), the angle vertical to \(x\) is \(x\) and the angle vertical to \(y\) is \(y\). Also, the adjacent angles to \(x\) and \(y\) in the linear - pair relationships will be \(y\) and \(x\) respectively.

Step2: Analyze option A

In option A, the angle relationships are correctly labeled. The vertical angles are equal (\(x\) with \(x\) and \(y\) with \(y\)) and the linear - pair relationships are maintained (\(x + y = 180^{\circ}\)).

Step3: Analyze option B

In option B, the angle relationships are incorrect. The angles that should be equal to \(x\) and \(y\) based on vertical - angle and linear - pair relationships are mislabeled.

Answer:

A.