Question

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

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal, vertical angles are equal and adjacent angles that form 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 the \(x^{\circ}\) angle (that forms a straight - line with it) is \(y^{\circ}\).

Step2: Analyze each option

In option A, the angle - labeling does not follow the vertical - angle and supplementary - angle relationships correctly. In option B, the angle - labeling is consistent with vertical angles being equal and adjacent angles being supplementary. In option C, the labeling is incorrect as it does not maintain the correct relationships. In option D, the labeling is also incorrect.

Answer:

B.