Answer:
[tex]\theta=\dfrac{3\pi}{4}[/tex]
Step-by-step explanation:
The formula for length of intercepted arc is
[tex]s=r\theta[/tex]
where, r is the radius of the circle and θ in the central angle in radian.
Radius of the circle = 48 millimeters
Length of intercepted arc = 36π millimeters
Substitute the given values in the above formula.
[tex]36\pi=48\theta[/tex]
Divide both sides by 48.
[tex]\dfrac{36\pi}{48}=\dfrac{48\theta}{48}[/tex]
[tex]\dfrac{3\pi}{4}=\theta[/tex]
Therefore, the measure of central angle is [tex]\theta=\dfrac{3\pi}{4}[/tex].
