Angle C and Angle D are vertical angles. The conclusion is that angle C and angle D are complementary. Which is a counterexample of this conclusion.
* 2 vertical angles which are not complementary
or
* 2 complementary angles which are not vertical
Ans. = A.
To find a counterexample for the conclusion that angle C and angle D are complementary, we need to look for a situation where angle C and angle D are vertical angles but not complementary. Remember that vertical angles are formed by a pair of intersecting lines and are congruent to each other, while complementary angles add up to a sum of 90 degrees.
Counterexample: Two vertical angles which are not complementary
Imagine a scenario with two intersecting lines forming angle C and angle D. Let angle C measure 40 degrees, and angle D measure 50 degrees. In this case, angle C and angle D are vertical angles, but they do not add up to 90 degrees and, therefore, are not complementary.
Alternatively, the conclusion does not state that vertical angles must be complementary. Thus, another counterexample could involve two complementary angles that are not vertical. Suppose we have two angles, angle C and angle D, measuring 30 degrees and 60 degrees, respectively. In this case, angle C and angle D are complementary, as they add up to 90 degrees. However, they are not vertical angles.
Both of these examples serve as counterexamples to the conclusion that angle C and angle D being vertical angles implies that they are complementary.