Question

which diagram below 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

• For the first diagram: The angles are adjacent but not supplementary (sum is not \(180^{\circ}\)).
• For the second diagram: The angles are not supplementary (sum is not \(180^{\circ}\)).
• For the third diagram: \(\angle1+\angle2 = 180^{\circ}\) (supplementary) and \(\angle1=\angle2 = 90^{\circ}\) (congruent).
• For the fourth diagram: The angles are vertical angles (not supplementary in the sense of the statement's context, as vertical angles are equal but their sum is not \(180^{\circ}\) unless they are \(90^{\circ}\) each, but this diagram doesn't show that).

Answer:

The third diagram (the one with \(\angle1\) and \(\angle2\) forming a straight - angle and being right angles) provides a counterexample.