Bunuel wrote:

The circle shown above has center O and radius of length 5. If the area of the shaded region is 20π, what is the value of x?

(A) 18

(B) 36

(C) 45

(D) 54

(E) 72

Attachment:

2017-11-16_1236_002.png

To find x, we need to know the measure of the unshaded reguon's central angle.

Then we would have two of the three angle measures of the triangle, where x is the third angle.

Find the central angle using the unshaded part's area as a portion or fraction of the circle's area.

Area of circle with radius 5 = \(25\pi\)

Area of shaded region, given: \(20\pi\)

Area of unshaded region: \(25\pi - 20\pi = 5\pi\)

Find the unshaded sector's fractional amount of the circle.

\(\frac{SectorArea}{CircleArea}=\frac{CentralAngle}{360°}\)

\(\frac{5\pi}{25\pi}=\frac{1}{5}=\frac{CentralAngle}{360°}\)

\(\frac{1}{5}\) of 360 is 72°. The right triangle's second angle = 90°.

x = (180 - 90 - 72) = 18 degrees

Answer A

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