Question

Mr. Thomas wrote these true statements.

If a figure is a triangle, the sum of the figure's interior angles is 180.
Figure ABC is a triangle.

Which conclusion can be drawn?

Using the law of detachment, the sum of the interior angles of ABC is 180.
Using the law of detachment, if the sum of a figure’s interior angles is 180, then the figure is a triangle.
Using inductive reasoning, the sum of the interior angles of ABC is 180.
Using inductive reasoning, if the sum of a figure’s interior angles is 180, then the figure is a triangle.

Answer 1

Correct conclusion: "Using the law of detachment, the sum of the interior angles of ABC is 180."

Reason: From "If a figure is a triangle, then its interior angles sum to 180" and the fact "ABC is a triangle," by modus ponens (law of detachment) you conclude "the interior angles of ABC sum to 180." The other statements either reverse the implication (invalid) or use inductive reasoning (not applicable).