Question

use the law of syllogism to determine a valid conclusion from the set of statements, if possible. select valid conclusion or no valid conclusion and explain your reasoning.
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.
valid conclusion select choice
select choice
the conclusion of statement (1) is not the hypothesis of statement (2).
if an angle is not acute, then the measure of the angle is between 90° and 180°
if the measure of an angle is between 90° and 180°, then the angle is not acute.

Explanation:

The Law of Syllogism states that if we have two conditional statements \(p
ightarrow q\) and \(q
ightarrow r\), then we can conclude \(p
ightarrow r\). Here, let \(p\) be "the measure of an angle is between \(90^{\circ}\) and \(180^{\circ}\)", \(q\) be "it is obtuse", and \(r\) be "it is not acute". The first statement is \(p
ightarrow q\) and the second is \(q
ightarrow r\). By the Law of Syllogism, we can combine them.

Answer:

If the measure of an angle is between \(90^{\circ}\) and \(180^{\circ}\), then the angle is not acute.