Open traverse ABCDEFG, deflection angles

For an open traverse whose last line has been observed independently, the bearing of the last line computed through the deflection angles must agree with the observed bearing. Right deflection is taken as $+$ and left as $-$.

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 = 28°33′. The observed back bearing of FG is 209°33′, so its observed FB is 209°33′ − 180° = 29°33′.

Step 2: Angular misclosure

$$\text{Misclosure} = \text{observed} - \text{computed} = 29^\circ 33' - 28^\circ 33' = +1^\circ 00'$$

The computed and observed bearings do not agree, so the observations of the deflection angles are not correct. The misclosure of +1°00′ is distributed equally among the 5 angles (+12′ each).

Step 3: Adjustment

Correction per angle = +1°00′ / 5 = +0°12′. The correction to a line is +0°12′ multiplied by the number of angles used to reach it.

Check: the corrected BB of the last line equals the observed value 209°33′.

Corrected deflection angles

The correction of +12′ is applied to each signed deflection angle (right $+$, left $-$), so a right deflection becomes 12′ larger and a left deflection 12′ smaller.

Answer: misclosure = +1°00′ (observations not correct). Corrected bearings: AB 40°45′, BC 67°34′, CD 1°01′, DE 22°09′, EF 56°15′, FG 29°33′. Corrected deflection angles: B 26°49′ R, C 66°33′ L, D 21°08′ R, E 34°06′ R, F 26°42′ L.