Following up Benoît Kloeckner's remarks, 
I include two images below, the first from the paper,
"Least-perimeter partitions of the disk into three regions of given areas"
([arXiv abs link](http://arxiv.org/abs/math/0307207)), the second from 
D'Arcy Thompson's *On Growth and Form*:
<hr />
![3partition][1]
<hr />
![DarcyThompson][2]
<hr />
Thompson explains the circumstances in which $120^\circ$ angles are preferred
in some regions of the wing
over the more prevalent $90^\circ$ angles.
The three arcs in the disk in Fig.1 meet at $120^\circ$,
and meet the circumcircle at $90^\circ$.


  [1]: https://i.sstatic.net/OZBSm.png
  [2]: https://i.sstatic.net/KpDG7.png