Question

what conclusion can be drawn from the given statements by using the law of syllogism? given: if the measure of an angle is between 90° and 180°, then it is obtuse. if an angle is obtuse, then it is not acute. choose the correct answer. a) if an angle is not acute, then it is obtuse. b) if the measure of an angle is between 90° and 180°, then it is not acute. c) if an angle is not acute, then the measure of the angle is between 90° and 180°. d) no valid conclusion can be drawn. the conclusion of the first statement is not the hypothesis of the second statement.

Explanation:

Step1: Identify statements

Let \(p\): The measure of an angle is between 90° and 180°. Let \(q\): The angle is obtuse. Let \(r\): The angle is not acute.

Step2: Analyze the Law of Syllogism

The first statement is \(p
ightarrow q\) (If the measure of an angle is between 90° and 180°, then it is obtuse). The second statement is \(q
ightarrow r\) (If an angle is obtuse, then it is not acute).

Step3: Apply the Law of Syllogism

By the Law of Syllogism (\(p
ightarrow q\) and \(q
ightarrow r\) implies \(p
ightarrow r\)), we get that if the measure of an angle is between 90° and 180°, then it is not acute.

Answer:

B. If the measure of an angle is between 90° and 180°, then it is not acute.