---
title: "Interior angles and bearings, closed traverse ABCD"
subject: "Surveying I"
chapter: 4
key: "semester_3/surveying_i:interior-angles-closed-traverse-104-30"
source: https://www.bctengineer.com/q/semester_3/surveying_i/interior-angles-closed-traverse-104-30
site: BCT Engineering
---

# Interior angles and bearings, closed traverse ABCD

Surveying I · Chapter 4: The Compass

- Asked in: 2064 Jestha, 10 marks
- Video: [Compass Surveying - Problem No 7 ( Reduced Bearing Type - Interior Angles & Adjustment of Bearings )](https://www.youtube.com/watch?v=uSgAKKkZZ08) — Stan Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/interior-angles-closed-traverse-104-30
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4

## Question

The observed fore and back bearings of the lines of a closed compass traverse are as follows.

| Line | FB | BB |
|---|---|---|
| AB | 104°30′ | 284°30′ |
| BC | 48°00′ | 226°00′ |
| CD | 290°30′ | 115°15′ |
| DA | 180°15′ | 357°30′ |

Calculate the interior angles and correct them. Also compute the correct bearings of all the sides.

## Short answer

Interior angles from observed bearings: A=107°00′, B=123°30′, C=64°30′, D=65°00′ (sum 360°, no correction needed). Corrected FB: AB 104°30′, BC 48°00′, CD 292°30′, DA 177°30′.

## Answer

Line AB has FB − BB = 180°00′, so stations A and B are free; stations C and D are corrected starting from it.

Local attraction at a station is detected by comparing the fore bearing (FB) and back bearing (BB) of each line: if there is no local attraction at either end, $\text{FB} - \text{BB} = 180^\circ$ exactly.

#### Step 1: Check each line

| Line | FB | BB | FB − BB | Remark |
|---|---|---|---|---|
| AB | 104°30′ | 284°30′ | 180°00′ | Free, difference = 180° |
| BC | 48°00′ | 226°00′ | 182°00′ | Differs by +2°00′ |
| CD | 290°30′ | 115°15′ | 175°15′ | Differs by −4°45′ |
| DA | 180°15′ | 357°30′ | 182°45′ | Differs by +2°45′ |

Line AB has a difference of exactly 180°, so stations A and B are free from local attraction. The other stations are corrected one after another, starting from B.

#### Step 2: Correct the stations in turn

- Line BC: FB at B = 48°00′ is correct. The correct BB is 228°00′, observed 226°00′, so the correction at C is +2°00′.
- Line CD: FB at C = 290°30′ with correction +2°00′ gives 292°30′. The correct BB is 112°30′, observed 115°15′, so the correction at D is −2°45′.
- Line DA (check): FB at D = 180°15′ with correction −2°45′ gives 177°30′. The correct BB is 357°30′, which equals the observed value, so A needs no correction, as expected.

| Station | A | B | C | D |
|---|---|---|---|---|
| Correction | 0 | 0 | +2°00′ | −2°45′ |

Stations affected by local attraction: C, D.

#### Step 3: Corrected bearings

| Line | Observed FB | Correction | Corrected FB | Observed BB | Corrected BB |
|---|---|---|---|---|---|
| AB | 104°30′ | 0 | 104°30′ | 284°30′ | 284°30′ |
| BC | 48°00′ | 0 | 48°00′ | 226°00′ | 228°00′ |
| CD | 290°30′ | +2°00′ | 292°30′ | 115°15′ | 112°30′ |
| DA | 180°15′ | −2°45′ | 177°30′ | 357°30′ | 357°30′ |

Check: corrected FB − corrected BB = 180° for every line.

#### Interior angles

The included angle at a station is found from the observed bearings taken at that station (FB of the leaving line minus BB of the arriving line), so local attraction does not affect it:

| Station | Working | Interior angle |
|---|---|---|
| A | 104°30′ − 357°30′ + 360° | 107°00′ |
| B | 48°00′ − 284°30′ + 360° | 123°30′ |
| C | 290°30′ − 226°00′ | 64°30′ |
| D | 180°15′ − 115°15′ | 65°00′ |

Sum = 360°00′ = $(2\times4-4)\times 90^\circ$, so the angles need **no correction**. They agree with the angles obtained from the corrected bearings.

**Answer:** Interior angles A = 107°00′, B = 123°30′, C = 64°30′, D = 65°00′ (no correction needed). Corrected bearings (FB): AB = 104°30′, BC = 48°00′, CD = 292°30′, DA = 177°30′.

## Check yourself

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

1. Why are the corrections in this traverse started from line AB?
   A. AB is the longest line
   B. AB has FB − BB = 180°, so A and B are free from local attraction
   C. AB is the first line alphabetically and always free
   D. AB has the smallest bearing
   Answer: B. A line whose FB and BB differ by exactly 180° has no attraction at either end, so its stations are the reliable starting point. (Key point: Starting line)

2. FB of CD is 290°30′ and C has a correction of +2°00′. The observed BB of CD is 115°15′. What is the correction at D?
   A. +2°45′
   B. −2°45′
   C. +4°45′
   D. −4°45′
   Answer: B. The corrected FB is 292°30′, so the correct BB is 112°30′. Observed 115°15′ is too large by 2°45′, so the correction is −2°45′. (Key point: Correction at D)

3. Which stations are affected by local attraction in this traverse?
   A. A and B
   B. B and C
   C. C and D
   D. A, B, C and D
   Answer: C. A and B are free (AB differs by 180°). The corrections found are +2°00′ at C and −2°45′ at D. (Key point: Stations affected)

4. The interior angles of this four-sided closed traverse are 107°00′, 123°30′, 64°30′ and 65°00′. What does their sum show?
   A. Sum is 360° = (2n − 4) × 90°, so no angular correction is needed
   B. Sum is 180°, so the traverse is open
   C. Sum is not 540°, so the angles are wrong
   D. The sum shows local attraction at every station
   Answer: A. For n = 4 the sum must be (2×4 − 4)×90° = 360°. The angles sum to exactly 360°, so no correction is needed. (Key point: Check on interior angles)

## Related in Surveying I

- [Local attraction: AB 69°30′ compass traverse](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ab-69-30-reordered) — Surveying I, chapter 4
- [Corrected bearings and interior angles, PQRST](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Acorrected-bearings-quadrantal-pq-s37-30e) — Surveying I, chapter 4
- [Local attraction, bearings AB 305°00′ (EA 45°)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ea-305-00) — Surveying I, chapter 4, asked 2×
- [Local attraction, bearings AB 305°30′](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ea-bb-44-00) — Surveying I, chapter 4, asked 2×
- [Local attraction and true bearings, 1°30′E](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Acompass-closed-traverse-declination-1-30-east) — 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×

## Related in other subjects

- [Bearings of BC and CD in traverse ABCDE](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-abcde-bearings-bc-cd) — Surveying II, chapter 1, asked 2×
- [Closed traverse missing EA bearing, BC length](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcdea-missing-ea-bc) — Surveying II, chapter 1
- [Missing bearings of BC and DE in traverse](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-missing-bearings-bc-de) — Surveying II, chapter 1
- [Hardy-Cross network discharge AB, BC, AD, CD](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ahardy-cross-as69) — Water Supply Engineering, chapter 7