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Answer:120 degrees

Arc length SRT is 1/6th(2 pi/12 pi) of the total circumference.
So angle POQ is 1/6*360= 60 degrees

That implies x+y= 180-60=120 degrees
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Bunuel

In the figure above, O is the center of the circle and arc SRT has length 2π. If the circumference of the circle is 12π, what is the value of x + y?

(A) 60
(B) 90
(C) 120
(D) 150
(E) cannot be determined from the information given


Attachment:
2017-11-23_2026_002.png
Sector ORT, whose arc is SRT, is a fraction of the circle. Let its central angle POQ = ∠Z. From the fraction \(\frac{Sector}{Circle}\), find ∠Z's measure to find (x + y)

\(\frac{ArcLength}{Circumference}=\frac{Part}{Whole}=\frac{SectorAngleZ}{360}\)

\(\frac{2\pi}{12\pi}=\frac{1}{6}=\frac{Z}{360}\)

\(6Z = 360\) , \(Z = 60\)

\(∆ OPQ: (x + y + Z) = 180\)
\(x + y + 60 = 180\)
\(x + y = 120\)


Answer C
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