Final answer:
A regular polygon that has a central angle of 40° has 9 sides. This is calculated by dividing the total central angle measurement of a circle (360°) by the central angle of the polygon.
Step-by-step explanation:
The question asks for the number of sides of a regular polygon with a central angle of 40°. In a regular polygon, the sum of the central angles is 360° since they form a circle around the center point. To find the number of sides of the polygon, we divide 360° by the central angle of the polygon:
Number of sides = 360° / Central angle
Number of sides = 360° / 40°
Number of sides = 9
Therefore, a regular polygon with a central angle of 40° has 9 sides.