--- title: "Link traverse ABCDEF, right turn angles" subject: "Surveying I" chapter: 4 key: "semester_3/surveying_i:link-traverse-right-turn-angles-22-17" source: https://www.bctengineer.com/q/semester_3/surveying_i/link-traverse-right-turn-angles-22-17 site: BCT Engineering --- # Link traverse ABCDEF, right turn angles Surveying I · Chapter 4: The Compass - Asked in: 2080 Baisakh, 6 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/link-traverse-right-turn-angles-22-17 - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4 ## Question The fore bearing of line AB of a link traverse ABCDEF is 61°06′00″. The right turn angles at stations with theodolite were observed as follows: ∠B = 93°06′50″, ∠C = -204°14′30″, ∠D = -112°50′20″ and ∠E = 90°58′20″. If the BB of the last line observed was 22°17′20″, check whether the observations for angles are correct or not. If not, compute the correct bearings of all lines. The value of C is 20″. ## Short answer Misclosure +80″ exceeds the permissible 40″, so observations are not correct. Corrected fore bearings: AB 61°06′00″, BC 334°13′10″, CD 358°28′00″, DE 291°18′40″, EF 202°17′20″ (back bearing 22°17′20″ matches observed). ## Answer Right-turn angles (measured clockwise from the back station to the forward station) are always positive, between $0^\circ$ and $360^\circ$. The "−" signs printed before ∠C and ∠D are therefore read as dashes, so ∠C = 204°14′30″ and ∠D = 112°50′20″. (If they are treated as negative angles, the computed bearing of the last line misses the observed one by 85°49′, which is impossible for a real traverse; with the angles read as positive, the misclosure is only 1′20″, which confirms this reading.) Angles used: B = 93°06′50″, C = 204°14′30″, D = 112°50′20″, E = 90°58′20″. **Rule (angles to the right):** $\text{FB of next line} = \text{FB of previous line} + 180^\circ + \text{angle to the right}$ (add or subtract $360^\circ$ to bring the result between $0^\circ$ and $360^\circ$). #### Step 1: Bearings computed from the observed angles | Line | Working | Computed FB | |---|---|---| | AB | given | 61°06′00″ | | BC | 61°06′00″ + 180° + 93°06′50″ | 334°12′50″ | | CD | 334°12′50″ + 180° + 204°14′30″ − 360° | 358°27′20″ | | DE | 358°27′20″ + 180° + 112°50′20″ − 360° | 291°17′40″ | | EF | 291°17′40″ + 180° + 90°58′20″ − 360° | 202°16′00″ | Computed FB of EF = 202°16′00″, so the computed BB of EF = 22°16′00″. The observed BB of EF is 22°17′20″ (observed FB = 202°17′20″). (Check: sum of angles = 501°10′00″; 61°06′00″ + 501°10′00″ + 4 × 180° = 1282°16′00″, and 1282°16′00″ − 3 × 360° = 202°16′00″.) #### Step 2: Angular misclosure $$ \text{Misclosure} = \text{observed} - \text{computed} = 22^\circ 17' 20'' - 22^\circ 16' 00'' = +1' 20'' = +80'' $$ Permissible misclosure $= C\sqrt{n} = 20''\sqrt{4} = 40''$. Since $80'' > 40''$, the angle observations are **not correct** (the error is outside the allowable limit). Strictly, the angles should be re-observed; for the correction asked in the question, the error is distributed equally over the four angles: $+80''/4 = +20''$ per angle. #### Step 3: Corrected bearings The correction to a line is +20″ multiplied by the number of angles used to reach it. | Line | Computed FB | Correction | Corrected FB | Corrected BB | |---|---|---|---|---| | AB | 61°06′00″ | 0 | 61°06′00″ | 241°06′00″ | | BC | 334°12′50″ | +20″ | 334°13′10″ | 154°13′10″ | | CD | 358°27′20″ | +40″ | 358°28′00″ | 178°28′00″ | | DE | 291°17′40″ | +60″ | 291°18′40″ | 111°18′40″ | | EF | 202°16′00″ | +80″ | 202°17′20″ | 22°17′20″ | Check: the corrected BB of the last line equals the observed value 22°17′20″. Corrected angles: B = 93°07′10″, C = 204°14′50″, D = 112°50′40″, E = 90°58′40″. **Answer:** misclosure = +80″, which exceeds the permissible 40″, so the observations are not correct. Corrected bearings (FB): AB 61°06′00″, BC 334°13′10″, CD 358°28′00″, DE 291°18′40″, EF 202°17′20″ (BB of EF = 22°17′20″). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Right-turn angle -204°14'30'' is equivalent to: A. 204°14'30'' B. 24°14'30'' C. 115°45'30'' D. 155°45'30'' Answer: D. Adding 360° gives 155°45'30''. (Key point: Negative angle conversion) 2. Observed BB of EF = 22°17'20''. Observed FB of EF is: A. 202°17'20'' B. 22°17'20'' C. 112°17'20'' D. 337°42'40'' Answer: A. FB = BB + 180° since BB < 180°. (Key point: Observed FB of last line) 3. The misclosure is about 85°49'. Compared with permissible 40'' it is: A. Within limits B. Far larger, so a blunder exists C. Equal to it D. Smaller, so adjust equally Answer: B. Such a large misclosure cannot be distributed; a blunder must be found. (Key point: Misclosure size) 4. What should be done with this data? A. Distribute 85° equally over angles B. Ignore the last bearing C. Re-check and re-observe; do not distribute the error D. Add 85° to every angle Answer: C. Only small errors within the permissible limit are adjusted. (Key point: Action) ## Close variants set in other exams - [Link traverse ABCDEF, last line 108°05′40″](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-abcdef-108-05-40) — Surveying I, chapter 4, asked 3× ## Related in Surveying I - [Link traverse XP to TY, angles to right](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-xp-ty-angles-to-right) — Surveying I, chapter 4 - [Open traverse ABCDEFGH, deflection angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aopen-traverse-deflection-angles-81-45) — Surveying I, chapter 4, asked 2× - [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 - [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 - [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 - [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× ## Related in other subjects - [Link traverse Q to X, Gale's table m1, m2](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alink-traverse-qx-gale-m1-m2) — Surveying II, chapter 1 - [Bowditch link traverse XABCY (X 1877.51 N)](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Abowditch-link-traverse-xabcy-1877) — Surveying II, chapter 1 - [Bowditch balancing of link traverse XABCY](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Abowditch-link-traverse-xabcy) — Surveying II, chapter 1, asked 2× - [Bowditch link traverse XABCY (X 1162.510 N)](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Abowditch-link-traverse-xabcy-1162) — Surveying II, chapter 1, asked 2×