Mon February 18, 2013 By:

if we divide 90 degree into 60 and 30 then wont it be a trisection of an angle?

Expert Reply
Mon February 18, 2013
Yes, you are right. Dividing a  90 degree into 60 degree and then into a 30 degree will give us 3 angles of 30 degree each and this indeed would be called as trisecting an angle.
However, that does not mean that trisection of any angle is possible by only a compass and ruler. Generally it is known that for any positive integer N, an angle of measure 2(pi)/N can be trisected only if 3 does not divide N. So, in this case for 90 degree angle, N will be 4 which is not divisible by 3. 
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