Connecting "out of system" roads?
There ARE integer sided triangles that have angles of 60 or 120 degrees, see here : https://en.wikipedia.org/wiki/Eisenstein_triple but I'm not sure how this helps you for building roads.
45 degrees there indeed aren't any. 
A progress of going one stud forward one stud left will get you 45 degrees if working studs on top. In case of SNOT 2 studs forward, 5 plates will also progress in an angle of 45 degrees.
There are elements that let you progress half a plate, so 1 stud to 2.5 plates works also.
For 60 or 30 degrees, the tangent is irrational so no 'precise' or exact progression exists, but it can probably fairly well be approximated. 
There are technic pieces called angular connectors that make angles that are multiples of 22.5 degrees. Also several connectors that make multiples of 60 degrees.
Also hinges that "click" in angles of 22.5 degrees...

Update: picture of angular connectors 

you would additionally need technic axles and bricks having axle holes:


But there are lots of other ways to connect the connectors, e.g. bricks with pin holes and a half-axle pin, half pins with stud, axles with stud,...