---
title: "Angular misclosure, link traverse ABCDEFG"
subject: "Surveying I"
chapter: 4
key: "semester_3/surveying_i:link-traverse-initial-154-50-last-335-30"
source: https://www.bctengineer.com/q/semester_3/surveying_i/link-traverse-initial-154-50-last-335-30
site: BCT Engineering
---

# Angular misclosure, link traverse ABCDEFG

Surveying I · Chapter 4: The Compass

- Asked in: 2081 Baisakh, 6 marks
- Video: [Link traverse numerical ||surveying-1 ||compass traverse](https://www.youtube.com/watch?v=2POiE9wgtmA) —  The civil classroom
- 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-initial-154-50-last-335-30
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4

## Question

The bearing of initial line (AB) = 154°50′ and the bearing of last line (FG) = 335°30′. The angles measured were ∠B = -164°40′, ∠C = +92°10′, ∠D = -65°50′, ∠E = +29°20′ and ∠F = -69°20′. The traverse is named ABCDEFG. Compute the angular misclosure, if any, on that traverse and the adjusted bearings of the traverse lines. Least count = 30′.

## Short answer

Using deflection angles (right positive, left negative): computed bearing of FG is 336°30′; given 335°30′ gives misclosure –1°00′ (permissible ±1°07′). Correction –12′ per angle yields adjusted bearings: AB 154°50′, BC 349°58′, CD 81°56′, DE 15°54′, EF 45°02′, FG 335°30′.

## Answer

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

| Line | Working | Computed FB |
|---|---|---|
| AB | given | 154°50′ |
| BC | 154°50′ − 164°40′ + 360° | 350°10′ |
| CD | 350°10′ + 92°10′ − 360° | 82°20′ |
| DE | 82°20′ − 65°50′ | 16°30′ |
| EF | 16°30′ + 29°20′ | 45°50′ |
| FG | 45°50′ − 69°20′ + 360° | 336°30′ |

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.

| Line | Computed FB | Correction | Corrected FB | Corrected BB |
|---|---|---|---|---|
| AB | 154°50′ | 0 | 154°50′ | 334°50′ |
| BC | 350°10′ | −0°12′ | 349°58′ | 169°58′ |
| CD | 82°20′ | −0°24′ | 81°56′ | 261°56′ |
| DE | 16°30′ | −0°36′ | 15°54′ | 195°54′ |
| EF | 45°50′ | −0°48′ | 45°02′ | 225°02′ |
| FG | 336°30′ | −1°00′ | 335°30′ | 155°30′ |

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′.

## Check yourself

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

1. Which sign is used for deflection angles?
   A. Right is -, left is +
   B. Both are +
   C. Right is +, left is -
   D. Both are -
   Answer: C. FB next = FB previous ± deflection with R as +. (Key point: Deflection rule)

2. Given FG = 335°30', computed = 336°30'. Misclosure is:
   A. +1°00'
   B. -1°30'
   C. 0
   D. -1°00'
   Answer: D. Given - computed = -1°00'. (Key point: Misclosure)

3. L.C. = 30' and n = 5 gives permissible misclosure about:
   A. 67' (1°07')
   B. 150'
   C. 30'
   D. 15'
   Answer: A. 30' x sqrt(5) = 67'. (Key point: Permissible misclosure)

4. The correction per angle is:
   A. -60'
   B. -12'
   C. -20'
   D. -15'
   Answer: B. -1°00' / 5 = -12' per angle, accumulated down the lines. (Key point: Adjustment)

## Related in Surveying I

- [Link traverse ABCDEF, last line 108°05′40″](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-abcdef-108-05-40) — Surveying I, chapter 4, asked 3×
- [Open traverse ABCDEFG, deflection angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aopen-traverse-deflection-angles-40-45) — Surveying I, chapter 4, asked 2×
- [Link traverse PABCQ: permissible misclosure](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-pabcq-permissible-misclosure) — 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
- [Link traverse ABCDEF, right turn angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-right-turn-angles-22-17) — Surveying I, chapter 4, asked 3×
- [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

## 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
- [AVL tree for 10 20 30 50 45 40 8 5 3](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Aavl-build-10-20-30) — Data Structure and Algorithm, chapter 6