Will give brainlist The radius of a circle is 40 miles. What is the angle measure of an arc 9pi miles long?

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:

=

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