---
title: "Link traverse PABCQ: permissible misclosure"
subject: "Surveying I"
chapter: 4
key: "semester_3/surveying_i:link-traverse-pabcq-permissible-misclosure"
source: https://www.bctengineer.com/q/semester_3/surveying_i/link-traverse-pabcq-permissible-misclosure
site: BCT Engineering
---

# Link traverse PABCQ: permissible misclosure

Surveying I · Chapter 4: The Compass

- Asked in: 2078 Bhadra, 6 marks
- Video: [How to correct angular Misclosure in traverse (closed loop)](https://www.youtube.com/watch?v=-DUmFgynmEE) — Mining Rabbi
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/link-traverse-pabcq-permissible-misclosure
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4

## Question

Determine the permissible angular misclosure and adjusted bearings in the following link traverse PABCQ. Bearing of line PA = 30°15′ and bearing of line QC = 225°45′. The deflection angles measured are ΔA = +100°30′, ΔB = +135°45′ and ΔC = +140°00′. Least count = 30′.

## Short answer

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

## Answer

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

| Line | Working | Computed FB |
|---|---|---|
| PA | given | 30°15′ |
| AB | 30°15′ + 100°30′ | 130°45′ |
| BC | 130°45′ + 135°45′ | 266°30′ |
| CQ | 266°30′ + 140°00′ − 360° | 46°30′ |

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.

| Line | Computed FB | Correction | Corrected FB | Corrected BB |
|---|---|---|---|---|
| PA | 30°15′ | 0 | 30°15′ | 210°15′ |
| AB | 130°45′ | −0°15′ | 130°30′ | 310°30′ |
| BC | 266°30′ | −0°30′ | 266°00′ | 86°00′ |
| CQ | 46°30′ | −0°45′ | 45°45′ | 225°45′ |

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′).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. QC = 225°45'. FB of CQ is:
   A. 45°45'
   B. 225°45'
   C. 135°45'
   D. 405°45'
   Answer: A. CQ is the reverse direction: 225°45' - 180° = 45°45'. (Key point: FB of last line)

2. Computed CQ = 46°30', known = 45°45'. Misclosure is:
   A. +45'
   B. -45'
   C. -52'
   D. -15'
   Answer: B. Given - computed = -45'. (Key point: Misclosure)

3. L.C. = 30' and n = 3 gives:
   A. 90'
   B. 30'
   C. 52'
   D. 17'
   Answer: C. 30' x sqrt(3) = 52'. (Key point: Permissible misclosure)

4. Since 45' < 52', the work is:
   A. Rejected and re-observed
   B. Corrected only at the last angle
   C. Corrected with +15' per angle
   D. Accepted; -15' per angle applied cumulatively
   Answer: D. -45'/3 = -15' per angle: AB -15', BC -30', CQ -45'. (Key point: Adjustment)

## Related in Surveying I

- [Angular misclosure, link traverse ABCDEFG](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-initial-154-50-last-335-30) — Surveying I, chapter 4
- [Link traverse XP to TY, angles to right](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-xp-ty-angles-to-right) — Surveying I, chapter 4
- [Corrected bearings, closed link traverse T1-T2](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-link-traverse-t1-t2-corrected-bearings) — Surveying I, chapter 4
- [Angle misclosure, closed link traverse AT1-ET2](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-link-traverse-at1-et2) — Surveying I, chapter 4
- [Adjusted angles and bearings, angles to the left](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aadjusted-angles-bearings-left-angles-aw-dx) — Surveying I, chapter 4
- [Open traverse ABCDEFGH, deflection angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aopen-traverse-deflection-angles-81-45) — Surveying I, chapter 4, asked 2×

## Related in other subjects

- [Closed loop/link traverse, misclosure terms](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-loop-link-traverse-misclosure) — Surveying II, chapter 1
- [Closed loop/link traverse, misclosure balancing](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-loop-link-traverse-angular-misclosure) — Surveying II, chapter 1
- [Link traverse B to M, coordinates X and Y](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alink-traverse-bowditch-x-y-between) — Surveying II, chapter 1
- [Adjust traverse A-X to E-Y bearings](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-adjust-latitude-departure-ax-ey) — Surveying II, chapter 1