Back Azimuth

An azimuth is a direction measured clockwise from north, running 0° to 360°, and the back azimuth is the same line looked at from the other end. The rule is add 180° if the azimuth is under 180°, subtract 180° if it is over, which is one rule, not two, once you take the result modulo 360°. Surveyors need it constantly because a traverse leg measured from A to B has to be carried forward from B, and because the check on a closed traverse is that the back azimuth of the last leg reproduces the first bearing you started from.

Bearings are the older notation and behave differently: a bearing of N 30° E has a back bearing of S 30° W, the same numeric angle with both letters flipped. Azimuths avoid all that quadrant bookkeeping, which is why modern instruments and coordinate geometry work in them. A worked example: a property line runs at azimuth 45°, so its back azimuth is 225°; a line at azimuth 300° reverses to 120°. Note that a magnetic back azimuth taken in the field will not agree with a computed one to better than the local declination and the compass's own reversal error, which is why the check is done on the numbers, not the needle.