Link traverse PABCQ: permissible misclosure

The bearings of the first line (PA) and the last line (QC) are known. Starting from PA, the bearing of CQ is computed through the deflection angles (right $+$). The bearing of line QC = 225°45′ is measured from Q towards C, so the FB of CQ = 225°45′ − 180° = 45°45′.

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 CQ = 46°30′; known FB of CQ = 45°45′.

Step 2: Angular misclosure

$$\text{Misclosure} = \text{known} - \text{computed} = -0^\circ 45'$$

Permissible misclosure $= L.C. \times \sqrt{n} = 30' \times \sqrt{3} = 52'$ (n = 3 angles). The misclosure of 45′ is less than 52′, so the work is acceptable and the error is distributed equally (−15′ per angle).

Step 3: Adjustment

Correction per angle = −0°45′ / 3 = −0°15′. The correction to a line is −0°15′ multiplied by the number of angles used to reach it.

Check: the corrected FB of the last line equals the known value 45°45′.

Answer: permissible angular misclosure = 52′ (actual −45′, acceptable). Adjusted bearings: PA 30°15′, AB 130°30′, BC 266°00′, CQ 45°45′ (QC 225°45′).