Angle Construction [self-discovered]

[Phlembac Adib Hasan]

Suppose $k\in \mathbb{N}$. Prove that we can construct all the angles of the form $\dfrac {\pi k} {60} $ using only a straitedge and a compass.
Hint:

No calculation, no difficult theorem; just logic.I discovered this beautiful thing about two and a half years ago when I was in class 6 and knew nothing of mathematics.