In the figure above, what fraction of the circle with center
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Angles opposite one another have the same measurement. Thus, both nonshaded regions measure 45 degrees from the center of the circle, for a total of 90 degrees.
A circle is 360 degrees, so 90 degrees is 1/4 of the circle that is unshaded. That leaves 3/4 of the circle shaded.
The answer is D.
A circle is 360 degrees, so 90 degrees is 1/4 of the circle that is unshaded. That leaves 3/4 of the circle shaded.
The answer is D.
Ceilidh Erickson
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Since the central angle of each white region is 45 degrees, the central angle of each shaded region is 180  45 = 135. Thus, (135 + 135)/360 = 270/360 = 3/4 is shaded.
Alternate Solution:
A sector corresponding to 45Â° will have an area which is 1/8 of the complete circle. The unshaded region consists of two such sectors; therefore, the unshaded region is 1/8 + 1/8 = 1/4 of the whole circle. Thus, the shaded region is 1  1/4 = 3/4 of the whole circle.
Answer: D
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