Question

which statement is true about this argument?
premises:
if an angle measure is between 90° and 180°, then the angle is an obtuse angle.
the measure of ∠c is 102°.
conclusion:
∠c is an obtuse angle.
the argument is not valid because the premises are not true.
the argument is not valid because the conclusion does not follow from the premises
the argument is valid by the law of syllogism.
the argument is valid by the law of detachment.

Explanation:

Step1: Recall the law of detachment

If \(p
ightarrow q\) (if \(p\) then \(q\)) is a true conditional statement and \(p\) (the hypothesis) is true, then \(q\) (the conclusion) is true.

Step2: Identify \(p\) and \(q\) in the given argument

Let \(p\): An angle measure is between \(90^{\circ}\) and \(180^{\circ}\). Let \(q\): The angle is an obtuse angle. The first premise is \(p
ightarrow q\). The second premise is \(p\) (since \(m\angle C = 102^{\circ}\) which means \(90^{\circ}<102^{\circ}<180^{\circ}\)).

Step3: Apply the law of detachment

By the law of detachment, since \(p
ightarrow q\) is true (by the definition of an obtuse angle) and \(p\) (for \(\angle C\)) is true, then \(q\) ( \(\angle C\) is an obtuse angle) is true.

Answer:

The argument is valid by the law of detachment.