Balancing angles of closed traverses

The sum of of the interior angles (if measured perfectly) is given by this formula:

where n is the number of angles measured and a is an angle

The maximum allowable error for measuring foreshots and backshots is

where k is the smallest division readable on the compass

Procedure for correcting angles

1. Calculate the "perfect" sum of interior angles and the sum of your measured (observed) angles.
2. If the difference is greater than the maximum allowable error, you will need to correct the data. This is done either by making a new set of measurements or calculating correction based on existing data.
3. To correct the azimuths:
   1. Compute the difference between the theortically perfect sum and the measured sum of interior angles
   2. Divide by the number of angles
   3. Add (or subtract) the correction factor to each azimuth or interior angle so that the new interior angles sum to the "perfect" value.

Notes:

There are other methods to correct angular measurement error, but for this exercise we will use this, the most common method.

Never make an adjustment that is smaller than the measurement accuracy of your device.