Question

For a circle with a radius of 6 feet, what is the measurement of the central angle (in degrees) that intercepts an arc

Answer 1

Answer: The central angle measures 135 degrees

Step-by-step explanation: We have been given an arc with length 9pi/2 feet and a radius of 6 feet. The arc is shown in the attached diagram (please see attachment). The central angle subtended by this arc is at point O and has been labeled angle X.

So if the diagram shows arc AB with length 9pi/2 and radius AO with length 6, we can use the formula to compute “Length of an arc” to arrive at the missing angle.

Length of an arc = X/360 x 2pi x radius

Substituting for the known values, our formula can now be re-written as

9pi/2 = X/360 x 2pi x6

By cross multiplication we now have

9pi/2pi x 6 = 2X/360

We simplify as much as possible by dividing all like terms, hence pi divides pi on the left side of the equation. Also 2 divides 360 on the right side of the equation.We now arrive at,

9/12 = X/180

Simplify even further and we have

3/4 = X/180

By cross multiplication we now have

(3 x 180)/4 = X

540/4 = X

135 = X

Therefore the central angle that intercepts the arc measures 135 degrees.