Angles and Fractions of a Circle

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

Review: Angles and Fractions of a Circle


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,



half the span of the circle. Thus, and . Since the full span of a circle is 360 degrees, the angle x spans a fraction of .

The correct answer is (B).


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