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

Explanation:

The converse of a conditional statement "if p then q" is "if q then p". Given the converse "if the sum of the exterior angles of a figure is 360°, then the figure is a polygon", the original conditional statement is "if the figure is a polygon, then the sum of the exterior angles of the figure is 360°". The inverse of a conditional statement "if p then q" is "if not p then not q". So the inverse of the original conditional statement is "if a figure is not a polygon, then the sum of the exterior angles is not 360°".

Answer:

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