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

Explanation:

A conditional statement is of the form "If \(p\), then \(q\)". The converse is "If \(q\), then \(p\)". Given the converse "If the sum of the exterior angles of a figure is \(360^{\circ}\), then the figure is a polygon", the original conditional statement is "If a figure is a polygon, then the sum of the exterior angles is \(360^{\circ}\)".
The inverse of a conditional statement "If \(p\), then \(q\)" is "If not \(p\), then not \(q\)".

Answer:

If the sum of the exterior angles of a figure is not \(360^{\circ}\), then the figure is not a polygon.