Effect on phase angle due to resistance
Consider this diagram where \$|R| = |X_L|\$: -



The following has to be true: -


The voltage across the resistor (red arrow) and the voltage across the inductor (blue arrow) have to spatially add-up to equal the supply voltage (black arrow). That addition is shown by the dotted lines.
The red and blue voltage arrows have to be 90 degrees apart because both inductor (blue) and resistor (red) share the same current.
The current through both components (orange arrow) has to be 90 degrees lagging the inductor voltage (blue) AND simultaneously in phase with resistor voltage (red).


When |R| = |\$X_L\$|, there can be no other diagram that complies with the above requirements.

If L dominates or R dominates you get these scenarios: -



If you take these two scenarios to the extremes, you should see that: -


Current lags supply voltage by 90 degrees (no resistance)
Current becomes in phase with supply voltage (no inductance)


If we set the combined series impedance magnitude of R and L, \$\sqrt{R^2 +X_L^2}\$ to be a constant, we will see that the trajectories for \$V_R\$ and \$V_L\$ follow circular paths: -



For the scenarios above, the current will have a constant amplitude and be in phase with \$V_R\$.

In case you didn't realize, these are called phasor diagrams and can be re-arranged like so (for example): -



This should allow you to see why the impedance magnitude of a series inductor and resistor (same current) is \$\sqrt{R^2+X_L^2}\$. This is because the angle inside a semi-circle is always 90°.