Use less than, equal to, or greater than to complete this statement: The measure of each exterior angle of a regular 4-gon is ____ the measure of each exterior angle of a regular 9-gon.

is less than the measure

To determine the relationship between the measure of each exterior angle of a regular 4-gon and a regular 9-gon, we first need to understand some properties of these polygons.

A regular polygon is a polygon with all sides and angles equal. The sum of the exterior angles of any polygon is always 360 degrees. Therefore, for a regular polygon, the measure of each exterior angle is 360 degrees divided by the number of sides.

For a regular 4-gon (a square), the measure of each exterior angle is 360 degrees divided by 4, which equals 90 degrees.

For a regular 9-gon (a nonagon), the measure of each exterior angle is 360 degrees divided by 9, which equals 40 degrees.

Comparing these measures, we can conclude that the measure of each exterior angle of a regular 4-gon is greater than the measure of each exterior angle of a regular 9-gon.

So, to complete the statement, we can say: The measure of each exterior angle of a regular 4-gon is greater than the measure of each exterior angle of a regular 9-gon.