Answer:
40.5°
Step-by-step explanation:
So this problem is a ratio setup. First, you have to calculate the total circumference of the circle using the following formula:
c = 2πr
Where c is the circumference, and r is the radius of the circle. Therefore:
c = 2π(40)
Simplify:
c = 80π
Now if the arc is 9π miles long, then it's a fraction of the whole circle, which is 360° . We can set this up as follows:
[tex]\frac{9\pi }{80\pi }[/tex] = [tex]\frac{x}{360}[/tex]
Now if we cross-multiply to solve for x:
(9)(π)(360) = (80)(π)(x)
When simplified dividing by 10π :
9*36 = 8x
Simplfy.
324 = 8x
Solve for x.
x = 40.5
