Question

which diagram is a counterexample to the statement, “supplementary angles are never congruent.”

Explanation:

Step1: Recall definition of supplementary and congruent angles

Supplementary angles add up to 180 degrees. Congruent angles have equal measures.

Step2: Analyze each diagram

In the first diagram, the angles are right - angled and supplementary and congruent. In the second diagram, vertical angles are supplementary and congruent. In the third diagram, the right - angled supplementary angles are congruent. In the fourth diagram, two non - right supplementary angles can be congruent (e.g., two 90 - degree angles), but if they are non - right and unequal (e.g., 100 and 80 degrees), it is a counter - example.

Answer:

The fourth diagram.