Once my brother told me that construction of a $20^\circ$ angle with the help of a compass is impossible.
I searched for it on the net but I did not find anything about how to prove it.
Kindly prove or disprove the problem (and remember that I am asking for a $20^\circ angle$ exactly).
The basic angle in every construction using only ruler and compass is $\frac{\pi}{3}$. Every other angle can be constucted by bisecting this angle. Now note that $20^{\circ} = \frac{\pi}{9}$, i.e. three times the basic angle. It's been proven that angle trisection using ruler and compass is impossible, hence the proof.
You can read more about angle trisection here. Actually it's proven for $\frac{\pi}{9}$, that it's impossible to construct.
