™PQR and ™QRS are supplementary if
and only if m™PQR = m™QRS = 90°. true or false if false provide a couterexample
The statement is false. I will provide a counterexample to illustrate why.
Counterexample:
Let's consider the following scenario:
- ™PQR has a measure of 60°.
- ™QRS has a measure of 120°.
In this case, ™PQR and ™QRS are supplementary angles (since they add up to 180°), but their measures are not equal to 90°. Therefore, the statement "™PQR and ™QRS are supplementary if and only if m™PQR = m™QRS = 90°" is false.
False.
A counterexample is when m™PQR = 85° and m™QRS = 95°. In this case, even though the angles are supplementary (they add up to 180°), they are not both equal to 90°, so the statement is false.