Angle C and angle D are vertical angles. Conclusion is that angle C and angle D are complementary. What is a counterexample of the conclusion?
since vertical angles are equal, they are complementary only if they both are 45 degrees.
So, pick any other angle as a counterexample.
To find a counterexample to the conclusion that angle C and angle D are complementary, we need to provide a scenario where angle C and angle D are indeed vertical angles, but they are not complementary.
First, let's clarify what it means for angles to be vertical. Vertical angles are formed by two intersecting lines, where the angles opposite each other are known as vertical angles. These angles have equal measures.
Now, let's consider a counterexample. Suppose we have two intersecting lines, and angle C and angle D are vertical angles. However, let's say angle C measures 90 degrees and angle D measures 45 degrees.
In this case, angle C and angle D are vertical angles (opposite to each other), but they are not complementary angles. Complementary angles are two angles that add up to 90 degrees. Since angle C measures 90 degrees and angle D measures 45 degrees, they are not complementary.
Therefore, the counterexample to the conclusion that angle C and angle D are complementary is when angle C measures 90 degrees and angle D measures 45 degrees, while still being vertical angles.