Angles 60${}^o$ and 30${}^o$ can be constructed using a scale and compass.
1. Draw a line l.
2. With O as centre and with any convenient radius, draw an arc to cut line l at A.
3. With A as centre and with the same radius, draw an arc to cut the previous arc at B.
4. Join OB and extend.  $\angle AOB={60}^o$

5. To construct 30${}^o$ we bisect 60${}^o$. 
 The remaining two angles cannot be constructed without using a protractor.