ActionScript 3.0 :: Labeling Points (TextField) On Graph

I've made a graph application in AS3. You can plot points and then lines draw between the points to form a polyline/polygon. At each point a label (textfield) is dynamically placed to label that point, i.e. A for the first point B for the second etc. What I'm struggling to understand and properly implement is how to make sure the label is not being overlapped by a line using simple trigonometry. I'm calculating the acute angle for the intersection between the two lines at each point and then substracting 360 degrees from that to get the angle of reflex. At this point I get lost. How can I place a textfield at the middle of that angle of reflex (basically the opposite side of where the lines are drawing to). Or, is there a better strategy for placing the textfields and insuring they are not overlapped by the lines?