How to write a voltage in phasor form (using a reference-voltage)
Write v2 in Phasor Form using v1 as reference...

To find it without drawing phasors you just add/subtract \$\theta °\$ to/from all of your phasors where  \$\theta °\$ is the angle that when added/subtracted from your reference phasor will make it  \$0°\$.  In your case you can subtract \$10°\$ from each phasor (thus making \$v_1\$ your reference).
Making \$v_1\$ the reference means you adjust its angle to \$0°\$.  When you do this, the entire phasor diagram rotates with \$v_1\$ until \$v_1\$ is at the \$0°\$ position.
For example, below on the left are two arbitrary phasors \$V_X\$ and \$V_Y\$. On the right I have made \$V_X\$ the reference and put it at position \$0°\$.

What really matters with phasors is their position relative to each other.  Rotating the whole group around does not change their relationship to each other.  Further, you can use whatever angle you want as the reference.  Some folks use \$90°\$ so it is whatever you prefer.