--- title: "Methods of measuring horizontal angles" subject: "Surveying I" chapter: 7 key: "semester_3/surveying_i:methods-of-measuring-horizontal-angles" source: https://www.bctengineer.com/q/semester_3/surveying_i/methods-of-measuring-horizontal-angles site: BCT Engineering --- # Methods of measuring horizontal angles Surveying I · Chapter 7: Transit and Theodolite - Asked in: 2079 Bhadra, 1+3 marks; 2063 Baisakh, 8 marks (asked 2 times) - Video: [Horizontal and Vertical Angle Methods of Repetition and Reiteration](https://www.youtube.com/watch?v=l1zcme3ZzCs) — Ekeeda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/methods-of-measuring-horizontal-angles - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-7 ## Question What are the different methods of measuring horizontal angles in theodolite survey? Explain any one method with a supporting sketch. ## Short answer Methods: ordinary (single angle), repetition, direction (reiteration), and closing the horizon. The repetition method adds the same angle several times on the circle and reads only at start and end; the mean = accumulated angle / number of repetitions, reducing reading and graduation errors. A sketch shows swinging between A and B using upper and lower clamps. ## Answer #### Methods of measuring horizontal angles 1. **Ordinary (single angle) method:** the angle is measured once on each face, reading both verniers on A and B; the angle = difference of the readings. 2. **Repetition method:** one angle is added several times on the circle and the total is divided by the number of repetitions. It is used when a single angle must be measured very accurately. 3. **Direction (reiteration) method:** several directions are measured from a reference object and the angles are found as differences; it is used when many angles are measured at one station. 4. **Method of closing the horizon:** a special case of reiteration in which the sum of all the angles around the station must be 360 degrees. #### Repetition method **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 \ / \ / ------ O ------ (upper plate clamp: A -> B ; lower plate: B -> A) ``` The error of a single reading is divided by the number of repetitions, graduation errors are reduced because different parts of the circle are used, and fewer readings have to be taken. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In the repetition method, how is the final value of the angle obtained? A. Total accumulated angle divided by the number of repetitions B. Average of the first and last single readings C. Sum of readings on both faces D. Difference of the readings on A and B on one face Answer: A. The same angle is added several times on the circle; only the first and last readings are taken, and total / n gives the mean angle. (Key point: Repetition method idea) 2. Which method is best when many angles are to be measured at one station? A. Repetition method B. Direction (reiteration) method C. Ordinary single-angle method only D. Tangent method Answer: B. Directions to all objects are read from one reference object and angles are found as differences of directions. (Key point: When to use direction method) 3. What check does the method of closing the horizon give? A. Sum of angles around the station is 90 degrees B. Sum of all angles around the station must be 360 degrees C. Each angle must be equal D. Face left must equal face right Answer: B. Closing the horizon is a special case of reiteration; the angles around a point add up to 360 degrees, so any misclosure shows the error. (Key point: Closing the horizon) 4. In the repetition method, when swinging the telescope back from B to A (without changing the circle reading), which clamp is loosened? A. Upper clamp B. Vertical clamp C. Lower clamp D. Both clamps Answer: C. Loosening the lower clamp frees the whole instrument from the circle, so the upper plate stays clamped to the circle and the reading is unchanged. (Key point: Clamp use in repetition) ## Related in Surveying I - [Measuring horizontal and vertical angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ahorizontal-and-vertical-angle-methods) — Surveying I, chapter 7 - [Horizontal angles from field notes ABCDA (2065)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atheodolite-field-notes-abcda-65-shrawan) — Surveying I, chapter 7 - [Horizontal angles from field notes, triangle ABC](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atheodolite-field-notes-abc-64-jestha) — Surveying I, chapter 7 - [Mean horizontal angles, station O (P, Q, R)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Amean-horizontal-angles-o-pqrp) — Surveying I, chapter 7 - [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 - [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