Question

For a circle with a radius of 6 feet, what is the measurement of the central angle (in degrees) that intercepts an arc with a length of
9π
2
feet?

Answer 1

Answer:

135 degrees

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

$C=2\pi r$

we have

$r=6\ ft$

substitute

$C=2\pi (6)$

$C=12\pi\ ft$

step 2

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

so

using proportion

Find out the measurement of the central angle (in degrees) that intercepts an arc with a length of 9π/2 ft

$\frac{12\pi}{360^o}=\frac{(9\pi/2)}{x}\\\\x=360(9\pi/2)/12\pi\\\\x=135^o$