I dont really understand your question.
Angle is a real value between 0 and 360 that indeed starts to east and increases against the clock.
An angle to east is equal to 0 AND 360 as these are the same.
An angle to north is equal to 90.
An angle to west is equal to 180.
An angle to south is equal to 270.
If you want an angle to a point somewhere to the south-east, you have an angle pointing to 270 til 360 degrees.
415 degrees is exacly the middle.
Pointing north east is somewhere between 0 and 90 and 45 is the middle.
If you want the angle between the east of the map and the south of the map it could be a bit different.
If the map is a square, it is no big problem, but if it is not then you need something to determine it.
In GUI there is a function that can calculate the angle between 2 points.
I don't know how to get the size of the map because I haven't got an editor right now but that shouldnt be a problem.
This might have answered your question but I don't really know what you mean.