---
title: "Angle measurement by repetition method"
subject: "Surveying I"
chapter: 7
key: "semester_3/surveying_i:angle-by-repetition-method"
source: https://www.bctengineer.com/q/semester_3/surveying_i/angle-by-repetition-method
site: BCT Engineering
---

# Angle measurement by repetition method

Surveying I · Chapter 7: Transit and Theodolite

- Asked in: 2081 Baisakh, 4 marks; 2080 Bhadra, 4 marks (asked 2 times)
- Video: [Repetition Method by theodolite survey](https://www.youtube.com/watch?v=hND_zKylqRc) — BIG C
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/angle-by-repetition-method
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-7

## Question

Explain the measurement of a horizontal angle by the repetition method (including three repetitions of an angle and computing the mean angle).

## Short answer

The same horizontal angle is mechanically added by repeatedly sighting back to A with the lower clamp and swinging to B with the upper clamp, without resetting the circle. The total accumulated angle divided by three repetitions gives the mean; for the example, mean angle AOB = 62°25′09.0″.

## Answer

**Repetition method.** The same horizontal angle (say AOB) is added several times mechanically on the circle, and the circle is read only at the start and at the end. The mean angle = total accumulated angle / number of repetitions.

**Procedure (angle AOB, three repetitions)**

1. Set up, centre and level the theodolite at O, with the telescope on face left. Using the upper clamp and upper tangent screw, set vernier A to 0°00′00″ (or any convenient reading), and read both verniers (A and B).
2. Loosen the lower clamp, sight A, tighten the lower clamp and bisect A exactly with the lower tangent screw.
3. Loosen the **upper** clamp and swing the telescope clockwise to B. Clamp it and bisect B with the upper tangent screw. Read the verniers (the first value of the angle may be booked as a check).
4. Loosen the **lower** clamp, swing the telescope back to A, clamp it and bisect A with the lower tangent screw. The circle reading does not change, because the upper plate is clamped to the circle.
5. Loosen the upper clamp and sight B again; bisect it with the upper tangent screw. The reading now shows the angle added twice.
6. Repeat steps 4 and 5 once more for the third repetition. Read both verniers; the reading now shows the angle added three times.
7. Change face (transit the telescope to face right) and repeat the same three repetitions, usually swinging anticlockwise. Take the mean of both faces.

```text
   A                       B
    \ (upper plate)       /
     \                  /
      -------- O --------
   First: set to A, swing to B (upper clamp)
   Next: lower clamp, back to A, then upper again to B
```

| Face | Vernier | Initial reading | Final reading (after 3 repetitions) | Accumulated angle |
|---|---|---|---|---|
| Left | A | 0°00′20″ | 187°15′50″ | |
| | B | 180°00′20″ | 367°15′58″ (7°15′58″) | |
| | Mean | | | 187°15′34.0″ |
| Right | A | 0°00′00″ | 187°15′20″ | |
| | B | 180°00′20″ | 367°15′40″ (7°15′40″) | |
| | Mean | | | 187°15′20.0″ |

#### Computation (example)
For face left: accumulated angle = (187°15′50″ - 0°00′20″ + 367°15′58″ - 180°00′20″)/2 = 187°15′34.0″.
Angle (face left) = 187°15′34.0″ / 3 = 62°25′11.33″.

For face right: accumulated angle = 187°15′20.0″, angle = 62°25′06.67″.

$$
\text{Mean angle AOB} = \frac{62°25′11.33″ + 62°25′06.67″}{2} = 62°25′09.0″
$$

**Answer:** mean angle AOB = 62°25′09.0″.

The reading error of the circle is divided by the number of repetitions (here 3), so the final angle is more accurate than one from a single reading.

## Check yourself

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

1. What is the principle of the repetition method?
   A. Two verniers are averaged
   B. The angle is measured once with high precision
   C. The same angle is added several times on the circle and the total is divided by the number of repetitions
   D. Each repetition uses a different station
   Answer: C. The reading error is divided by the number of repetitions. (Key point: Principle)

2. Which clamp is loosened to go back to A for the second repetition?
   A. The upper clamp
   B. The vertical clamp
   C. The tripod screw
   D. The lower clamp
   Answer: D. The lower clamp frees the whole instrument, so the circle reading stays unchanged. (Key point: Clamps)

3. Face left accumulated angle is 187°15′34″ for three repetitions. What is the angle?
   A. 62°25′11.33″
   B. 62°25′05″
   C. 187°15′34″
   D. 93°37′47″
   Answer: A. 187°15′34″/3 = 62°25′11.33″. (Key point: Face left angle)

4. FL gives 62°25′11.33″ and FR 62°25′06.67″. What is the mean?
   A. 62°25′11.33″
   B. 62°25′09.0″
   C. 62°25′18″
   D. 62°25′04.6″
   Answer: B. (11.33+06.67)/2 = 9.0 seconds. (Key point: Mean angle)

## Related in Surveying I

- [Horizontal angle by repetition and direction methods](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Arepetition-and-direction-methods-field-notes) — Surveying I, chapter 7, asked 2×
- [Booking format for two-set horizontal angle](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Abooking-format-two-set-horizontal-angle) — Surveying I, chapter 7