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Bunuel

If O is the center of the circle above, what fraction of the circular region is encompassed by an angle of x degrees?

A. 1/36
B. 1/12
C. 1/9
D. 1/6
E. The answer cannot be determined from the given information.


Attachment:
image496.png

Official Explanation



In this question, the angles shown appear span half the circle. We can infer that they must, in fact, because the opposite angles of bisecting lines are equal. On the other side of each of the 2x angles shown is another 2x, and on the other side of each x shown is another x. Therefore,

2x + x + 2x + x = 180

Half the span of the circle. Thus, 6x = 180 and x = 30. Since the full span of a circle is 360 degrees, the angle x spans a fraction of 30/360 = 1/12.

The correct answer is (B).
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Bunuel

If O is the center of the circle above, what fraction of the circular region is encompassed by an angle of x degrees?

A. 1/36
B. 1/12
C. 1/9
D. 1/6
E. The answer cannot be determined from the given information.


Attachment:
image496.png

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From the figure, the given angles make up 180 degrees.

=> 6x = 180 => x=30.

The fraction encompassed by the angle x would x/360 => 30/360 = 1/12
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