Question

find the truth value of the conditional. explain your reasoning, or show a counterexample. if an angle measures 135°, then it is an obtuse angle. choose the correct answer below. a. it is possible for an angle to be obtuse without measuring 135°, so a counterexample exists. therefore, the conditional is false. b. the hypothesis is false since an angle cannot measure 135°. therefore, the conditional is true. c. if the hypothesis is true and an angle measures 135°, then it is an obtuse angle, and so the conclusion is also true. therefore, the conditional is true. d. if the conclusion is true and an angle is an obtuse angle, then it measures between 90° and 180°, and so the hypothesis is also true. therefore, the conditional is true.

Explanation:

An obtuse - angle is defined as an angle whose measure is between 90° and 180°. Since 135° is between 90° and 180°, if an angle measures 135°, it is an obtuse angle. In a conditional statement "if p then q", when the hypothesis p (an angle measures 135°) is true and the conclusion q (it is an obtuse angle) is also true, the conditional statement is true.

Answer:

C. If the hypothesis is true and an angle measures 135°, then it is an obtuse angle, and so the conclusion is also true. Therefore, the conditional is true.