Why we draw the angle with y-axis?

[Aladin]

When we want to indicate the direction of a vector,why we draw the angle with the vertical (y-axis) side?

 

[robphy]

Technically speaking, one can draw the angle with respect to any convenient reference direction... and, for clarity, you should somehow indicate that reference direction and sense (clockwise or counterclockwise). A clear diagram, as you've drawn, is fine.

Standard conventions usually use the counterclockwise angle from the positive x-axis. However, if you use anything else, do what I suggested above.