Link traverse ABCDEF, right turn angles

Right-turn angles (measured clockwise from the back station to the forward station) are always positive, between $0^\circ$ and $360^\circ$. The "−" signs printed before ∠C and ∠D are therefore read as dashes, so ∠C = 204°14′30″ and ∠D = 112°50′20″. (If they are treated as negative angles, the computed bearing of the last line misses the observed one by 85°49′, which is impossible for a real traverse; with the angles read as positive, the misclosure is only 1′20″, which confirms this reading.)

Angles used: B = 93°06′50″, C = 204°14′30″, D = 112°50′20″, E = 90°58′20″.

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

Step 1: Bearings computed from the observed angles

Computed FB of EF = 202°16′00″, so the computed BB of EF = 22°16′00″. The observed BB of EF is 22°17′20″ (observed FB = 202°17′20″).

(Check: sum of angles = 501°10′00″; 61°06′00″ + 501°10′00″ + 4 × 180° = 1282°16′00″, and 1282°16′00″ − 3 × 360° = 202°16′00″.)

Step 2: Angular misclosure

$$\text{Misclosure} = \text{observed} - \text{computed} = 22^\circ 17' 20'' - 22^\circ 16' 00'' = +1' 20'' = +80''$$

Permissible misclosure $= C\sqrt{n} = 20''\sqrt{4} = 40''$.

Since $80'' > 40''$, the angle observations are not correct (the error is outside the allowable limit). Strictly, the angles should be re-observed; for the correction asked in the question, the error is distributed equally over the four angles: $+80''/4 = +20''$ per angle.

Step 3: Corrected bearings

The correction to a line is +20″ multiplied by the number of angles used to reach it.

Check: the corrected BB of the last line equals the observed value 22°17′20″.

Corrected angles: B = 93°07′10″, C = 204°14′50″, D = 112°50′40″, E = 90°58′40″.

Answer: misclosure = +80″, which exceeds the permissible 40″, so the observations are not correct. Corrected bearings (FB): AB 61°06′00″, BC 334°13′10″, CD 358°28′00″, DE 291°18′40″, EF 202°17′20″ (BB of EF = 22°17′20″).