Answer:
[tex]\theta=\dfrac{4\pi}{9}[/tex] .
Step-by-step explanation:
Given information:
Radius = 10 feet
Area = [tex]\frac{200\pi}{9}[/tex] sq. ft. ...(i)
We need to find the measures of the central and inscribed angels for this sector.
The area of a sector is
[tex]A=\dfrac{1}{2}r^2\theta[/tex]
where, r is radius and [tex]\theta [/tex] is central angle in radian.
Substitute r = 10 in the above formula.
[tex]A=\dfrac{1}{2}(10)^2\theta[/tex]
[tex]A=50\theta[/tex] ...(ii)
From (i) and (ii), we get
[tex]50 \theta=\dfrac{200\pi}{9}[/tex]
[tex]\theta=\dfrac{200\pi}{9\times 50}[/tex]
[tex]\theta=\dfrac{4\pi}{9}[/tex]
Therefore, the measure of central angle is [tex]\dfrac{4\pi}{9}[/tex].
