Respuesta :
Answer:
The central angle measure of the sector is 150º.
Step-by-step explanation:
A sector of a circle is the portion of a circle enclosed by two radii and an arc.
When you know the central angle the area of a sector is given by
[tex]A=\pi r^2(\frac{C}{360} )[/tex]
where
r is the radius of the circle of which the sector is part.
C is the central angle in degrees.
We know that the area of the sector is [tex]60\pi \:cm^2[/tex] and the radius is 12 cm. Applying the above formula and solving for the central angle we get that
[tex]60\pi =\pi (12)^2(\frac{C}{360}) \\\\\pi \left(12\right)^2\left(\frac{C}{360}\right)=60\pi \\\\\frac{\pi 12^2\cdot \frac{C}{360}}{144\pi }=\frac{60\pi }{144\pi }\\\\\frac{C}{360}=\frac{5}{12}\\\\C=150[/tex]
