Answer:
135 degrees
Step-by-step explanation:
step 1
Find the circumference of the circle
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=6\ ft[/tex]
substitute
[tex]C=2\pi (6)[/tex]
[tex]C=12\pi\ ft[/tex]
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
[tex]\frac{12\pi}{360^o}=\frac{(9\pi/2)}{x}\\\\x=360(9\pi/2)/12\pi\\\\x=135^o[/tex]
