## Using compass, construct 1 deg arc on a circle, if 19 deg arc of this circle is given

Exercise #27 from a textbook called Kiselev's Geometry / Book I. Planimetry:

Using only compass, construct a 1 degree arc on a circle, if a 19 degree arc of this circle is given.

Please, check my reasoning on this one. I just want to make sure that I'm getting it right.

My solution:
Using a pair of compasses, we can only divide an angle in half. So long as we are given a 19 degree arc, we cannot really apply this method because we will end up having angles with fractional parts. But if we take a 19 degree angle 10 times we will get the angle of 190 degrees which we can divide in half and get an 80 degree angle, which in turn divided in half will give us a 40 degree angle, which again divided in half will give us a 20 degree angle. Now we can superimpose this 20 degree angle onto the 19 degree angle, which will give us by subtraction a 1 degree angle, that is a 1 degree arc.
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