The measurement of the central angle is 135 degrees
Solution:
The length of arc when angle given in degrees is given as:
[tex]Arc\ length = \frac{ \theta }{360} \times 2 \pi r[/tex]
Where,
r is the radius
[tex]\theta[/tex] is the central angle in degrees
From given,
[tex]r = 6\ feet\\\\Arc\ length = \frac{ 9 \pi }{2}\ feet[/tex]
Substituting the values we get,
[tex]\frac{9 \pi }{2} = \frac{ \theta }{ 360} \times 2 \times \pi \times 6\\\\9 \times 360= \theta \times 24\\\\\theta = 135[/tex]
Thus the measurement of the central angle is 135 degrees
