3. Azimuth from Interior Angles
Given the following traverse and horizontal angles:
Figure C28 
Using a azimuth of 68°00' for line OP, determine the azimuths of the remaining lines counterclockwise around the traverse.
At point P: 

Figure C29 
Line PQ is 92°48' right of Azimuth PO Az PO is the back azimuth of Az OP Az PQ = (Az OP + 180°00') + Angle PAz PQ = (68°00' + 180°00') + 92°48' = 340°48' 
At point Q: 

Figure C30 
Line QR is 112°26' to the right from Az QP Az QP is the back azimuth of Az PQ Az QR = (Az PQ + 180°00') + Angle QAz QR = (340°48'+180°00') + 112°26' = 633°14' Normalize: Az QR = 633°14'  360°00' = 273°14' 
At point R: 

Figure C31 
Line RO is 67°14' right from Az RQ Az RQ is the back azimuth of Az QR Az RO = (Az QR + 180°00') + Angle RAz RO = (273°14' + 180°00') + 67°14' = 520°28' Normalize: Az RO = 520°28'  360°00' = 160°28' 
The directions for all four traverse lines have been computed. Angles at P, R, and R have been used, but not the angle at O. For a math check, use Azimuth RO and the angle at O to compute the original Az OP. 

At point O: 

Figure C32 
Line OP is 87°32' right of Az OR Az OR is the back azimuth of Az RO Az OP = (Az RO + 180°00') + Angle O Az OP = (160°28' + 180°00') + 87°32' = 428°00' Normalize: Az OP = 428°00'  360°00' = 68°00' check! 
Summary:
Line  Bearing 
OP  68°00' 
PQ  340°48' 
QR  273°14' 
RO  160°28' 
There's a distinct pattern computing these azimuths:
New Az = (Previous Az + 180°00') + Angle.
This is true for a loop traverse meeting these conditions:
 Directions are counterclockwise around the traverse, and,
 Angles are interior to the right.
What if the directions are clockwise around the traverse and interior angles counterclockwise?
New Az = (Previous Az  180°00')  Angle
Other patterns exist for clockwise travel with clockwise interior angles, clockwise exterior angles, counterclockwise exterior angles, etc. Rather than memorize the possible patterns, draw a sketch, and begin computing; the pattern will present itself after a few lines.