Question

find the truth value of the conditional. explain your reasoning, or show a counterexample. if two angles are complementary, then their measures add up to 90°. choose the correct answer below. a. it is possible for the measures of complementary angles to add up to more than 90°, so a counterexample exists. therefore, the conditional is false. b. if the hypothesis is true and two angles are complementary, then their measures add up to 90°, and so the conclusion is also true. therefore, the conditional is true. c. the hypothesis is false since non - adjacent angles cannot be complementary. therefore, the conditional is true. d. if the conclusion is true and the measures of two angles add up to 90°, then they are complementary, and so the hypothesis is also true. therefore, the conditional is true.

Explanation:

By definition, complementary angles are two angles whose measures add up to 90°. If the hypothesis "two angles are complementary" is true, then by this definition, the conclusion "their measures add up to 90°" must also be true.

Answer:

B. If the hypothesis is true and two angles are complementary, then their measures add up to 90°, and so the conclusion is also true. Therefore, the conditional is true.