KöMaL 2012 C1142

The points $P$, $A$, $B$ and $Q$, in this order, lie on the same line such that $PA$=$BQ$, and a triangle ABC with interior angles of $36^o$, $72^o$, $72^o$ can be constructed out of the three line segments. Let $R$ be the intersection of the circle of radius $CP$ centred at $C$ and the extension of the line $AC$ beyond $C$. Find the angles subtended by the line segment $PQ$ at the points $C$ and $R$.