This would be an angle measured in standard position.
Assume the first point is at the origin. Then the difference in x values would be the x-coordinate of the second point and the difference in y-values would be its y-coordinate. Draw a quick sketch to see this. Then in the sketch you should be able to see a right triangle using the x-axis and a vertical to the second point.
Use this triangle to calculate the angle using right-triangle trig.
This gives the angle in standard position.
Note that you have taken the opposite of this twice, thus cancelling each other out. First, West is 0 degrees instead of East (as it would be in standard position). And second, North is at -90 degrees instead of South (as it would be in standard position).