Angular misclosure, link traverse ABCDEFG

In a link traverse starting and ending on lines of known bearing, the bearing of the last line computed from the observed deflection angles is compared with its known bearing. Right deflections are taken as $+$ and left deflections as $-$ (as given).

Rule (deflection angles): $\text{FB of next line} = \text{FB of previous line} \pm \text{deflection}$, with $+$ for a right deflection and $-$ for a left deflection.

Step 1: Bearings computed from the observed angles

Computed FB of FG = 336°30′; given (observed) FB of FG = 335°30′.

Step 2: Angular misclosure

$$\text{Misclosure} = \text{given} - \text{computed} = -1^\circ 00'$$

Permissible misclosure $= L.C.\times\sqrt{n} = 30'\sqrt{5} = 67'$ (about 1°07′), where $n = 5$ angles. The misclosure of −60′ (1°00′) is less than 67′, so the observations are accepted and the error is distributed equally.

Step 3: Adjustment

Total correction = −1°00′ (added to the computed bearing of the last line). It is distributed equally over the 5 observed angles: −1°00′ / 5 = −0°12′ per angle. The correction to a line is −0°12′ multiplied by the number of angles used to reach it.

Check: corrected FB of the last line equals the observed value 335°30′.

Answer: angular misclosure = −1°00′ (observed 335°30′, computed 336°30′), within permissible 1°07′. Adjusted bearings: AB 154°50′, BC 349°58′, CD 81°56′, DE 15°54′, EF 45°02′, FG 335°30′.