Link traverse ABCDEF, last line 108°05′40″

In a link traverse the bearing of the last line, computed from the first bearing and the observed angles, must agree with its observed bearing. The difference is the angular misclosure.

Rule (angles to the right): $\text{FB of next line} = \text{FB of previous line} + 180^\circ + \text{angle to the right}$ (subtract multiples of $360^\circ$ to bring the result between $0^\circ$ and $360^\circ$).

Step 1: Bearings computed from the observed angles

Step 2: Angular misclosure

The observed back bearing of EF is 108°05′40″, so its observed FB is 108°05′40″ + 180° = 288°05′40″.

$$\text{Misclosure} = \text{observed} - \text{computed} = 288^\circ 05'40'' - 288^\circ 06'20'' = -0^\circ 00'40''$$

So the angles are not exactly correct: there is a misclosure of 40″. Assuming a theodolite with least count $C = 20''$, the permissible misclosure is $C\sqrt{n} = 20''\sqrt{4} = 40''$, so the error is just within the limit and the angles are adjusted equally.

Step 3: Adjustment

The total correction is −0°00′40″. It is distributed equally over the 4 observed angles: −0°00′40″ / 4 = −0°00′10″ per angle. The correction to each line is −0°00′10″ multiplied by the number of angles used to reach it.

Check: the corrected FB of the last line equals the observed value, 288°05′40″.

Answer: misclosure = −40″ (the observations are not exactly correct, but are within the 40″ permissible limit). Corrected FBs: AB 61°06′00″, BC 334°12′40″, CD 309°58′00″, DE 17°07′30″, EF 288°05′40″ (the BBs differ by 180°; see the table).