Answer:
9
Step-by-step explanation:
The number of central angles in a regular polygon is always equal to the number of sides of the polygon.
Therefore, we have:
[tex]n[/tex] = number of central angles
[tex]N=[/tex] number of sides in the polygon
So
[tex]N=n[/tex]
We also know that the sum of the central angles in a polygon must be 360 degreeso, so we have:
[tex]n\theta = 360^{\circ}[/tex]
where
[tex]\theta[/tex] = measure of each central angle
Here we are told that
[tex]\theta=40^{\circ}[/tex]
So we can find the number of central angles:
[tex]n=\frac{360}{\theta}=\frac{360}{40}=9[/tex]
So, the polygon has 9 sides:
[tex]N=n=9[/tex]
