Question

which statement is true about this argument?
premises:
if a triangle has an angle that measures (150^{circ}), then it is an obtuse triangle.
(\triangle jkl) is an obtuse triangle.
conclusion:
(\triangle jkl) has an angle that measures (150^{circ}).
the argument is valid by the law of detachment.
the argument is valid by the law of syllogism.
the argument is not valid because the conclusion does not follow from the premises.
the argument is not valid because the premises are not true.

Explanation:

The law of detachment requires that if \(p
ightarrow q\) (if a triangle has an angle of \(150^{\circ}\), then it is obtuse) and \(p\) (triangle has \(150^{\circ}\) angle), then \(q\) (it is obtuse). Here, we have \(p
ightarrow q\) and \(q\) ( \(\triangle JKL\) is obtuse), trying to conclude \(p\) ( \(\triangle JKL\) has \(150^{\circ}\) angle). This is an invalid form of reasoning (affirming the consequent). A triangle can be obtuse ( \(q\)) with an angle other than \(150^{\circ}\) (e.g., \(120^{\circ}\)). So the conclusion does not follow from the premises.

Answer:

The argument is not valid because the conclusion does not follow from the premises.