What is the approximate measure, in degrees, of the central angle of the circle whose radius is 15 m and arc length is 10 m?

a. 38.22

b. 40.25

c. 42.99

d. 46.37

Option a.

The approximate measure, in degrees, of the central angle is

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

we have

assume

substitute

step 2

Using proportion

Find the central angle of the circle by and arc length of 10 m

Remember that the circumference of a circle subtends a central angle of 360 degrees

so

Let

x -----> the measure of the central angle in degrees

check the picture below.