Question

mr. thomas wrote these true statements. if a figure is a triangle, the sum of the figures 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 100°. using the law of detachment, if the sum of a figures 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 figures interior angles is 180°, then the figure is a triangle.

Explanation:

The law of detachment states that if \(p
ightarrow q\) (if a figure is a triangle (\(p\)), then the sum of its interior angles is \(180^{\circ}\) (\(q\))) and \(p\) (figure \(ABC\) is a triangle) are both true, then \(q\) (sum of interior angles of \(ABC\) is \(180^{\circ}\)) is true. Inductive reasoning is based on patterns of examples, which is not the case here. The first option has wrong sum (\(100^{\circ}\) instead of \(180^{\circ}\)). The second option reverses the implication. The fourth option uses inductive reasoning incorrectly.

Answer:

Using the law of detachment, the sum of the interior angles of \(ABC\) is \(180^{\circ}\) (but this option is not correctly labeled in the given choices. Among the given options, there is an error in presentation. If we assume the intended correct option is similar to the law - of - detachment application, but based on the given options' structure, there might be a mis - labeling. However, the correct logical conclusion using the law of detachment is that since \(ABC\) is a triangle (satisfying the hypothesis of the conditional statement "If a figure is a triangle, then the sum of its interior angles is \(180^{\circ}\)"), the sum of the interior angles of \(ABC\) is \(180^{\circ}\))