B. Balancing Angles

1. Angle Condition

a.Interior Angles

For a closed non-crossing loop traverse, the angle condition is: 



Equation B-1

Figure B-1
Angle Condtion - Loop
 A loop traverse which crosses itself doesn’t have conventional “interior” angles so Equation B-1 won’t work. Some other angle condition must be established for such cases.    b2
  Figure B-2
Crossling Traverse


b. Deflection Angles

If deflection angles are used, the angle condition depends on how many times, if any, the traverse crosses itself. 

 b3    b4
(a) Even crossings   (b) Odd crossings
Figure B-3
Deflection Angles
 img2    img3
Equation B-2   Equation B-3


Angle condition equations are exact so the 0°, 180°, and 360° in the equations are also exact.

c. Link Traverse

In order to determine angular misclosure for a closed link traverses, directions must be known at both ends:

Figure B-4
Link Traverse Angle Condition


This isn't the case for most link traverses, even those which begin and end on known points. Since it can't be identified, potential angular misclosure is addressed in the traverse adjustment.