Question

which diagram provides a counter - example to the following statement? \supplementary angles are never congruent.\

Explanation:

Step1: Recall supplementary and congruent angles

Supplementary angles add up to 180°. Congruent angles have equal measure.

Step2: Analyze each option

In the first option, angles 1 and 2 are supplementary but not congruent. In the second option, angles 1 and 2 are right - angles (90° each), they are supplementary (90°+90° = 180°) and congruent. In the third option, vertical angles 1 and 2 are congruent but not supplementary in most cases (except when they are right - angles).

Answer:

The second diagram (where angles 1 and 2 are right - angles) provides a counter - example to the statement "Supplementary angles are never congruent."