I went through three versions of the same question in different books and in one O is the center is not mentioned and in the others yes.

If x were equal to 90, the shaded region would have an area equal to 1/ 4 that of the entire circle (since 90 is 1/ 4 of 360). If the angle were equal to 90, the shaded region would have an area of \(4 \pi\) (1/ 4 of the entire circle’s area). Since the area of the shaded region is actually less than \(4 \pi\), x must be less than 90.

B is correct

Area of Circle =\(π\)\(r^2\)

\(16π\) = \(π\)\(r^2\)

\(r= 4\)

Now, Area of shaded region < \(4π\)

\(\frac{x}{360}\)\(π\)\(r^2\) < 4\(π\)

\(\frac{x}{360}\)\( π\)16 < 4\(π\)

\(\frac{x}{90}\) < 1

x < 90

Hence, B

I went through three versions of the same question in different books and in one O is the center is not mentioned and in the others yes.

If x were equal to 90, the shaded region would have an area equal to 1/ 4 that of the entire circle (since 90 is 1/ 4 of 360). If the angle were equal to 90, the shaded region would have an area of \(4 \pi\) (1/ 4 of the entire circle’s area). Since the area of the shaded region is actually less than \(4 \pi\), x must be less than 90.

B is correct[/quote]

Thank you Carcass

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