Answer: 9
Step-by-step explanation: The number of sides that a regular polygon has can be determined by the measure of one of its exterior angles. A regular polygon is a polygon with sides of equal length and angles of equal measure.
The measure of one exterior angle of a regular polygon is equal to 360° divided by the number of sides of the polygon. Therefore, if one exterior angle of a regular polygon measures 40°, we can use the following equation to find the number of sides of the polygon:
exterior angle measure = 360° / number of sides
40° = 360° / number of sides
number of sides = 360° / 40°
number of sides = 9
Therefore, a regular polygon with one exterior angle measuring 40° has 9 sides.