HEDGE 36
why the heading change?
if you are on an airway the presumption is that there might be traffic below you and if you descended while on course you might collide.
a 45 degree or 90 degree turn takes you off the airway and away from potential traffic.
HOWEVER
in many places where radar is quite good, like in the good old USA, a descent on the airway will be noticed by ATC and they will radio conflicting traffic and have them turn.
leaving an airway means leaving the safety of an MEA etc.
some airlines teach it, others don't. depends.
I hope this answers your intelligent question. one of the few I've seen here.