Question

The converse of a conditional statement is "If the sum of the exterior angles of a figure is 360°, then the figure is a polygon.

” What is the inverse of the original conditional statement?

A. If a figure is a polygon, then the sum of the exterior angles is 360°.

B. If the sum of the exterior angles of a figure is not 360°, then the figure is not a polygon.

C. If the sum of the exterior angles of a figure is 360°, then the figure is not a polygon.

D. If a figure is not a polygon, then the sum of the exterior angles is not 360°.

Answer 1

The answer is D because the statement is saying it's not a polygon if the sum of the exterior angles is not 360 which is the opposite of the statement

Answer 2

The correct option is D.

Explanation:

Converse statement : If the sum of the exterior angles of a figure is 360°, then the figure is a polygon.

Now, to form a converse statement, the conclusion becomes the hypothesis and the hypothesis becomes the conclusion.

So, to form the original statement of the given converse statement : Hypothesis will become conclusion and the conclusion becomes our hypothesis.

⇒ Original Statement : The figure is a polygon if the sum of the exterior angles of a figure is 360°.

Now to form the inverse we need the negation of both hypothesis and the conclusion.

Hence, The inverse of the original statement is : If a figure is not a polygon, then the sum of the exterior angles is not 360°.

Therefore, The correct option is D.