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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?

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

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

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

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

Verified Answer :

madhattedlady

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:

The correct option is D.

Step-by-step 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.

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