I'm aware that, in general, arbitrary angles cannot be trisected by a compass and straightedge, but also that it is possible for some specific angles. I've been googling for a while to find:
- Which angles are trisectable, and
- What is the procedure for trisecting these angles
It is fairly easy to trisect a $90^\circ$ angle but how does one trisect a $27^\circ$ angle (which one link says is trisectable)? Is there a general method for trisecting angles that are trisectable?
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$\begingroup$There is no general method of trisecting an angle using compass and straightedge. The nine-degree angle can be constructed using compass and straightedge by first constructing a regular pentagon, for which the interior angle is 72°. Bisect this angle three times and you have a nine-degree angle.
Alternatively, construct a 81° by tripling your angle, construct a pentagon and subtract the 72° angle. You can always multiply your angle by an integer or bisect it.
To confuse matters a bit, a 3° is also constructable: create an hexagon and pentagon inside the same circle and the difference between the interior angles is 12°. Bisect this a couple of times and you get a 3°, which is the interior angle of a 120-gon. You can't do better than this for integral numbers of degrees.
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