Question

which diagram provides a counterexample to the statement below. supplementary angles are never congruent.

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\). Congruent angles are angles that have the same measure.

Step2: Analyze each diagram

• Diagram A: The sum of \(\angle1\) and \(\angle2\) is \(180^{\circ}\) (they form a linear - like pair). But they are not congruent.
• Diagram B: The sum of \(\angle1\) and \(\angle2\) is \(180^{\circ}\) (they form a linear - like pair). But they are not congruent.
• Diagram C: \(\angle1\) and \(\angle2\) are vertical angles. Vertical angles are congruent and also supplementary (since the sum of adjacent angles formed by two intersecting lines is \(180^{\circ}\), and vertical angles are equal, so \(2\angle1 = 180^{\circ}\), \(\angle1=\angle2 = 90^{\circ}\) in the case of intersecting lines forming supplementary vertical angles).
• Diagram D: \(\angle1\) is \(90^{\circ}\) and \(\angle2\) is \(90^{\circ}\), they are congruent and supplementary.

Answer:

B