Aregular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius. each of the central angles has a measure of 40°. how many sides does the polygon have?

EACH central angle = 360 / number of sides 
number of sides = 360 / each central angle 
number of sides = 360 / 40
number of sides = 9

The circle is drawn by rotating the point drawn 360 degrees. If the circle is divided into parts, where each angle measures 40 degrees, then you can determine the number of sides by dividing 360 by 40. The answer will be 9. Therefore, the polygon is a nonagon.