---
title: "Corrected bearings and included angles (65)"
subject: "Surveying I"
chapter: 4
key: "semester_3/surveying_i:local-attraction-included-angles-de-82-45"
source: https://www.bctengineer.com/q/semester_3/surveying_i/local-attraction-included-angles-de-82-45
site: BCT Engineering
---

# Corrected bearings and included angles (65)

Surveying I · Chapter 4: The Compass

- Asked in: 2065 Shrawan, 9 marks
- Video: [4.4 Compass Surveying: Calculation of BEARINGS from INCLUDED ANGLES](https://www.youtube.com/watch?v=rCJnRKfG1GA) — Civil Modules
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/local-attraction-included-angles-de-82-45
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4

## Question

Find the corrected bearings of the following traverse and also the included angles.

| Line | FB | BB |
|---|---|---|
| AB | 191°30′ | 13°00′ |
| BC | 69°30′ | 246°30′ |
| CD | 32°15′ | 210°30′ |
| DE | 262°45′ | 82°45′ |
| EA | 230°15′ | 53°00′ |

## Short answer

Line DE is free but direct correction fails, so the included-angle method is used. Interior angles sum 540°30′, correction −0°06′ each. Starting from DE 262°45′, corrected bearings: AB 188°33′, BC 64°57′, CD 30°36′, DE 262°45′, EA 230°09′. Included angles: A 138°24′, B 56°24′, C 145°39′, D 52°09′, E 147°24′.

## Answer

Line DE has FB − BB = 180°00′, so stations D and E are free. The other lines show errors (AB −1°30′, BC +3°00′, CD +1°45′, EA −2°45′), so **A, B and C are suspected**. Line EA differs by −2°45′ although E is free (by DE), which shows that the bearings also contain observational errors and not only local attraction. The station corrections do not agree when worked in the two directions round the traverse, so the included-angle method is used.

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 | 191°30′ | 13°00′ | 178°30′ | Differs by −1°30′ |
| BC | 69°30′ | 246°30′ | 183°00′ | Differs by +3°00′ |
| CD | 32°15′ | 210°30′ | 181°45′ | Differs by +1°45′ |
| DE | 262°45′ | 82°45′ | 180°00′ | Free, difference = 180° |
| EA | 230°15′ | 53°00′ | 177°15′ | Differs by −2°45′ |

#### Step 2: Included (interior) angles

The included angle at a station uses the FB of the line leaving it and the BB of the line arriving at it, both observed at the same station, so local attraction cancels in the angle.

The sum of the interior angles should be $(2n-4)\times 90^\circ = 540^\circ$.

| Station | Angle between | Observed | Corrected |
|---|---|---|---|
| A | AE and AB | 138°30′ | 138°24′ |
| B | BA and BC | 56°30′ | 56°24′ |
| C | CB and CD | 145°45′ | 145°39′ |
| D | DC and DE | 52°15′ | 52°09′ |
| E | ED and EA | 147°30′ | 147°24′ |

Sum observed = 540°30′; error = +0°30′; correction per angle = −0°06′ (equal distribution, since each angle is measured with the same care).

Line DE has FB − BB = 180°, so its bearing is free from local attraction and is taken as the starting line.

#### Step 3: Corrected bearings from the corrected angles

Rule used: FB of next line = BB of previous line + interior angle (traverse run anticlockwise). Starting from DE = 262°45′ (BB 82°45′): EA = 82°45′ + 147°24′ = 230°09′, and so on round the traverse.

| Line | Observed FB | Correction | Corrected FB | Observed BB | Corrected BB |
|---|---|---|---|---|---|
| AB | 191°30′ | −2°57′ | 188°33′ | 13°00′ | 8°33′ |
| BC | 69°30′ | −4°33′ | 64°57′ | 246°30′ | 244°57′ |
| CD | 32°15′ | −1°39′ | 30°36′ | 210°30′ | 210°36′ |
| DE | 262°45′ | 0 | 262°45′ | 82°45′ | 82°45′ |
| EA | 230°15′ | −0°06′ | 230°09′ | 53°00′ | 50°09′ |

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

#### Interior angles from the corrected bearings

| Station | Interior angle |
|---|---|
| A | 138°24′ |
| B | 56°24′ |
| C | 145°39′ |
| D | 52°09′ |
| E | 147°24′ |

Sum = 540°00′ (as required).

**Answer:** Corrected bearings (FB): AB = 188°33′, BC = 64°57′, CD = 30°36′, DE = 262°45′, EA = 230°09′. Included angles: A = 138°24′, B = 56°24′, C = 145°39′, D = 52°09′, E = 147°24′.

## Check yourself

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

1. DE has FB - BB = 180°. Which stations are suspected?
   A. A, B and C
   B. D and E
   C. B, C and D
   D. C, D and E
   Answer: A. D and E are free through line DE; A, B and C are suspected. (Key point: Free and suspected stations)

2. Line EA differs by -2°45′ although E is free. What does this show?
   A. Station E is actually attracted
   B. The bearings also contain observational errors, not only local attraction
   C. DE must have been misread
   D. Local attraction is always larger at free stations
   Answer: B. A free station cannot cause the discrepancy, so there are other errors too, and station corrections would disagree around the traverse; hence the included-angle method. (Key point: Observational errors)

3. The observed interior angles sum to 540°30′. What is the correction per angle?
   A. +0°06′
   B. -0°30′
   C. -0°06′
   D. -0°05′
   Answer: C. Error +30′ over 5 angles = 6′ each, subtracted. (Key point: Angle correction)

## 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
- [Local attraction, BC 79°30′ and DE 82°15′](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ab-191-30-bc-79-30) — Surveying I, chapter 4
- [Local attraction ABCDEA by included angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-abcdea-included-angle) — Surveying I, chapter 4, asked 2×
- [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×
- [Interior angles and bearings, closed traverse ABCD](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ainterior-angles-closed-traverse-104-30) — Surveying I, chapter 4
- [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×

## 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×
- [Bearings of DE and EA in traverse ABCDE](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-abcde-bearings-de-ea) — Surveying II, chapter 1, asked 2×
- [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
- [Design pipes AB and BC, A RL 210 m, 44 and 18 lps](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-c73) — Water Supply Engineering, chapter 7