Is the direction angle always measured from the plus x axis?

Does a vector in the +,+ quadrant always have a direction between 0 and 90,

and in -,+ between 90 and 180

and in -,- between 180 and 270

and in -,+ between 270 and 360

?

Also, how should we calculate the direction using tan? Would that mean nested if statements to find out what quadrant we're in, and then applying the appropriate "work arounds"? E.g. If we were in the -,+ (like in the diagram) would we find the angle from the + axis would be 90 + tan^-1(y/x), the 90 + only used because we're in the -,+ quadrant. Also, that's just a quick solution, may be off, I just want to know if we use nested if statements to get the angle from the + x axis.

Finally, should we find the distance in degrees or radians?