Phasor Diagram with AC circuits
I don´t understand some parts of your question, however I will try to answer it the best possible.

I consider that the angle of the voltage and current phasors in the shown diagram are given.

First thing to start with a diagram always is to set up your Kirchhoff laws, in this case the one for meshes:

$$ \underline{V} = \underline{V}_R + \underline{V}_L = R~\underline{I} + j \omega L ~ \underline{I} $$

Since the current through resistor and reactor is the same, you can see that the both partial voltages have to be orthogonal to each other. Also, you know that current and voltage in an resistor are in phase while voltage leads 90 degrees in a reactor. Now you should be able to construct the diagram. If the resistor voltage phasor is parallel to the current phasor and the sum of resistor and reactor end up at the same point as the source voltage, chances are high you did it right.