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There are at least two ways to find 1/4 of an angle. One is to measure the angle with a protractor and divide by 4. The other is to use Euclid's straight-edge-and-compass construction for the bisector of the angle. This gives half the angle. Then use the same construction again on the half angle to get one fourth of the original angle.

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Q: What measures 1 fourth of an angle?
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