---
title: "Quadrantal/WCB; declination, isogonic, agonic"
subject: "Surveying I"
chapter: 4
key: "semester_3/surveying_i:bearings-declination-isogonic-agonic"
source: https://www.bctengineer.com/q/semester_3/surveying_i/bearings-declination-isogonic-agonic
site: BCT Engineering
---

# Quadrantal/WCB; declination, isogonic, agonic

Surveying I · Chapter 4: The Compass

- Asked in: 2061 Baisakh, 6 marks
- Video: [Magnetic Declination # Isogonic Line # Agonic Line # Compass Survey.](https://www.youtube.com/watch?v=GSLSJaf6TFA) — Civil Samajh
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/bearings-declination-isogonic-agonic
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4

## Question

What are quadrantal and whole circle bearings? Explain magnetic declination, isogonic line and agonic line.

## Short answer

Whole circle bearing is measured clockwise from north 0°–360°; quadrantal bearing is an acute angle from N or S towards E or W. Magnetic declination is the angle between true and magnetic meridians. An isogonic line connects points of equal declination; the agonic line is the isogonic line with zero declination, where magnetic and true north coincide.

## Answer

#### Quadrantal and whole circle bearings

- **Whole circle bearing (WCB):** angle of a line from the north end of the meridian, clockwise, $0^\circ$–$360^\circ$ (prismatic compass).
- **Quadrantal bearing (QB):** acute angle from the nearest N or S end of the meridian towards E or W, written like N $35^\circ$ E (surveyor's compass).

| WCB | QB |
|---|---|
| $0^\circ$–$90^\circ$ | N $\theta$ E |
| $90^\circ$–$180^\circ$ | S $(180^\circ - \theta)$ E |
| $180^\circ$–$270^\circ$ | S $(\theta - 180^\circ)$ W |
| $270^\circ$–$360^\circ$ | N $(360^\circ - \theta)$ W |

#### Magnetic declination

The angle between the true meridian and the magnetic meridian at a place. East if the magnetic north is east of true north (positive), west if it is west (negative).

$$
\text{True bearing} = \text{Magnetic bearing} \pm \text{declination}
$$

#### Isogonic line

An imaginary line on a map (or the earth) joining places having the **same magnetic declination**.

#### Agonic line

The isogonic line along which the declination is **zero**, that is, where the magnetic and true meridians coincide. The magnetic bearing equals the true bearing on this line. Declination is east on one side of it and west on the other.

## Check yourself

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

1. A quadrantal bearing is:
   A. A clockwise angle up to 360°
   B. The difference of FB and BB
   C. An acute angle from the N or S end of the meridian towards E or W
   D. Always measured from the east
   Answer: C. QB lies between 0° and 90°, e.g. N 35° E. (Key point: QB definition)

2. WCB 300° corresponds to QB:
   A. N 30° W
   B. S 60° W
   C. N 60° E
   D. N 60° W
   Answer: D. NW quadrant: 360° - 300° = 60°, N 60° W. (Key point: QB from WCB)

3. An isogonic line joins places having:
   A. The same magnetic declination
   B. Zero declination only
   C. The same elevation
   D. The same latitude
   Answer: A. Iso = equal; isogonic lines connect equal declination. (Key point: Isogonic line)

4. On the agonic line:
   A. Declination is maximum
   B. Declination is zero, so magnetic bearing equals true bearing
   C. The needle dips vertically
   D. Local attraction is zero
   Answer: B. The agonic line is the isogonic line of zero declination. (Key point: Agonic line)

## Related in Surveying I

- [Corrected and true bearings, 5°E declination](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-true-bearings-5-deg) — Surveying I, chapter 4
- [Whole circle and reduced bearing](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Awhole-circle-and-reduced-bearing) — Surveying I, chapter 4
- [Define magnetic declination](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Adefine-magnetic-declination) — Surveying I, chapter 4
- [Variations in magnetic declination](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Avariations-in-magnetic-declination) — Surveying I, chapter 4
- [Local attraction with quadrantal bearings](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-quadrantal-bearings-s11-30w) — Surveying I, chapter 4
- [Bearings and local attraction explained](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Abearings-and-local-attraction-terms) — Surveying I, chapter 4, asked 2×

## Related in other subjects

- [Smaller area bounded by circle and line](https://www.bctengineer.com/question.md?key=semester_2%2Fmathematics%3Asmaller-area-bounded-circle-line) — Mathematics, chapter 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×
- [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 AB and EA from latitudes, departures](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alatitude-departure-bearings-ab-ea) — Surveying II, chapter 1