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An infinite number.

It is relatively simple to draw a perpendicular bisector and so you have a 90 degree angle. It is also simple to bisect an angle and so you can make a 45 deg angle and, if you add it to the other side of the 90 deg, a 135 deg angle. Bisect these and you can make 22.5 deg, 67.5 deg, 112.5 deg and 157.5 deg.

You can keep bisecting angles and adding them to either side of the angles that you have already got. In theory, there is no limit to the number of times this process can be repeated - except the lifespan of the universe.

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14y ago

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