---
title: "Horizontal angles from field notes ABCDA (2065)"
subject: "Surveying I"
chapter: 7
key: "semester_3/surveying_i:theodolite-field-notes-abcda-65-shrawan"
source: https://www.bctengineer.com/q/semester_3/surveying_i/theodolite-field-notes-abcda-65-shrawan
site: BCT Engineering
---

# Horizontal angles from field notes ABCDA (2065)

Surveying I · Chapter 7: Transit and Theodolite

- Asked in: 2065 Shrawan, 10 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/theodolite-field-notes-abcda-65-shrawan
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-7

## Question

The following are the field notes of theodolite survey on traverse ABCDA. Compute the horizontal angles and correct them if necessary.

| Station | Sighted to | Face Left | Face Right |
|---|---|---|---|
| A | D | 00°00′00″ | 179°59′50″ |
| | B | 60°42′20″ | 240°42′10″ |
| B | A | 00°00′00″ | 180°00′10″ |
| | C | 98°55′40″ | 278°55′50″ |
| C | B | 00°00′10″ | 180°00′00″ |
| | D | 82°12′30″ | 262°12′20″ |
| D | C | 00°00′10″ | 179°59′50″ |
| | A | 118°10′30″ | 298°10′10″ |

## Short answer

Mean angles: A 60°42′20″, B 98°55′40″, C 82°12′20″, D 118°10′20″. Sum 360°00′40″, error +40″; equal correction -10″ yields A = 60°42′10″, B = 98°55′30″, C = 82°12′10″, D = 118°10′10″.

## Answer

**Assumption:** closed traverse ABCDA (interior angles), so the sum must be 360°.

**Method.** For each target the mean direction is found from the two faces:

$$
\text{Mean direction} = \frac{\text{Face L} + (\text{Face R} \pm 180^\circ)}{2}
$$

The angle at a station = mean direction of the forward station - mean direction of the back station. For a closed traverse of $n$ sides, the sum of the interior angles must be $(n-2) \times 180^\circ$; the difference is the angular error, which is distributed equally among the angles (the angles are measured with the same instrument and care).

#### Field book and mean angles
| Inst. stn | Sighted to | Face L | Face R | Mean direction | Mean angle |
|---|---|---|---|---|---|
| A | D | 00°00′00″ | 179°59′50″ | 359°59′55″ | |
| | B | 60°42′20″ | 240°42′10″ | 60°42′15″ | **60°42′20″** |
| B | A | 00°00′00″ | 180°00′10″ | 0°00′05″ | |
| | C | 98°55′40″ | 278°55′50″ | 98°55′45″ | **98°55′40″** |
| C | B | 00°00′10″ | 180°00′00″ | 0°00′05″ | |
| | D | 82°12′30″ | 262°12′20″ | 82°12′25″ | **82°12′20″** |
| D | C | 00°00′10″ | 179°59′50″ | 0°00′00″ | |
| | A | 118°10′30″ | 298°10′10″ | 118°10′20″ | **118°10′20″** |

#### Check and adjustment
Required sum = $(4-2) \times 180^\circ$ = 360°00′00″.
Observed sum = 360°00′40″.
Angular error = 360°00′40″ - 360°00′00″ = +0°00′40″.
Correction per angle = -0°00′10″ (equal for all 4 angles).

| Angle at | Mean angle | Correction | Corrected angle |
|---|---|---|---|
| A | 60°42′20″ | -0°00′10″ | **60°42′10″** |
| B | 98°55′40″ | -0°00′10″ | **98°55′30″** |
| C | 82°12′20″ | -0°00′10″ | **82°12′10″** |
| D | 118°10′20″ | -0°00′10″ | **118°10′10″** |
| Sum | 360°00′40″ | -0°00′40″ | 360°00′00″ |

**Answer:** corrected horizontal angles: A = 60°42′10″, B = 98°55′30″, C = 82°12′10″, D = 118°10′10″.

## Check yourself

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

1. How is the mean direction to a target found from the two face readings?
   A. [Face L + (Face R -/+ 180°)] / 2
   B. Face L + Face R
   C. Face L - Face R
   D. (Face L + Face R) / 360°
   Answer: A. Face R differs from Face L by 180°, so it is brought back by 180° and averaged with Face L. (Key point: Mean direction formula)

2. At A, Face R for D is 179°59′50″. What is the mean direction to D (Face L 0°00′00″)?
   A. 0°00′05″
   B. 359°59′55″ (i.e. -5″)
   C. 179°59′55″
   D. 0°00′10″
   Answer: B. Face R - 180° = -10″; mean of 0 and -10″ is -5″ = 359°59′55″. (Key point: Mean direction near zero)

3. The mean angles total 360°00′40″. What is the error and correction per angle?
   A. -40″ error; +10″ to each angle
   B. +40″ error; -40″ to one angle
   C. +40″ error; -10″ to each angle
   D. +40″ error; -13.3″ to each angle
   Answer: C. The sum exceeds 360° by 40″, shared among 4 angles = 10″ each. (Key point: Angular error)

4. After correction, what is the angle at A?
   A. 60°42′30″
   B. 60°42′20″
   C. 60°41′40″
   D. 60°42′10″
   Answer: D. 60°42′20″ - 10″ = 60°42′10″. (Key point: Corrected angles)

## Related in Surveying I

- [Mean angles and VCR, station O (reading 179°59′40″)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Amean-direction-o-abcd-first-reversed-179-59-40) — Surveying I, chapter 7, asked 3×
- [Theodolite traverse ABCDA with missing VCR (68°30′10″)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atheodolite-traverse-abcda-hcr-vcr-68-30-10) — Surveying I, chapter 7
- [Mean angles, traverse ABCDA (2068 Baisakh)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Amean-horizontal-angles-abcda-hcr-209-25-40) — Surveying I, chapter 7, asked 2×
- [Mean angles, traverse ABCDA (2074 Asoj)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Amean-horizontal-angles-abcda-hcr-90-00-00-a-d) — Surveying I, chapter 7, asked 2×
- [Mean angles, traverse ABCDA (2076)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Amean-horizontal-angles-abcda-hcr-90-00-20-c-b) — Surveying I, chapter 7, asked 2×
- [Theodolite traverse ABCDA, booking format with VCR](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atraverse-abcda-booking-format-vcr-120-14-20) — Surveying I, chapter 7

## Related in other subjects

- [Gale's table for traverse ABCDA](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Agale-table-abcda-2072a) — Surveying II, chapter 1
- [Closed traverse ABCDA missing data, C(1200, 2000)](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcda-c-1200-2000) — Surveying II, chapter 1
- [Closed traverse ABCDA missing figures (C=2500)](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcda-missing-2072m) — Surveying II, chapter 1
- [Closed traverse ABCDA, missing data](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcda-missing-2069b) — Surveying II, chapter 1