---
title: "Link traverse XP to TY, angles to right"
subject: "Surveying I"
chapter: 4
key: "semester_3/surveying_i:link-traverse-xp-ty-angles-to-right"
source: https://www.bctengineer.com/q/semester_3/surveying_i/link-traverse-xp-ty-angles-to-right
site: BCT Engineering
---

# Link traverse XP to TY, angles to right

Surveying I · Chapter 4: The Compass

- Asked in: 2067 Asar, 9 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-xp-ty-angles-to-right
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4

## Question

The following angles to the right were obtained in a closed link traverse between two adjusted known lines XP and TY. Compute the angular misclosure, if any, on that traverse and the adjusted bearings of the traverse lines.

| Station | Angle to the right | Bearing |
|---|---|---|
| X | | |
| P | 92°30′ | 148°15′ |
| Q | 228°30′ | |
| R | 115°15′ | |
| S | 52°45′ | |
| T | 298°45′ | |
| Y | | 36°45′ |

## Short answer

Angular misclosure is +0°45′. Adjusted bearings: XP 148°15′, PQ 60°54′, QR 109°33′, RS 44°57′, ST 277°51′, TY 36°45′.

## Answer

Reading of the table: 148°15′ is the adjusted bearing of the known line XP and 36°45′ is the adjusted bearing of the known line TY. Angles are measured to the right at P, Q, R, S, T, so the bearing of the next line = bearing of the previous line + 180° + angle.

**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 |
|---|---|---|
| XP | given | 148°15′ |
| PQ | 148°15′ + 180° + 92°30′ − 360° | 60°45′ |
| QR | 60°45′ + 180° + 228°30′ − 360° | 109°15′ |
| RS | 109°15′ + 180° + 115°15′ − 360° | 44°30′ |
| ST | 44°30′ + 180° + 52°45′ | 277°15′ |
| TY | 277°15′ + 180° + 298°45′ − 720° | 36°00′ |

Computed FB of TY = 36°00′; given (observed) FB of TY = 36°45′.

#### Step 2: Angular misclosure

$$
\text{Misclosure} = \text{given} - \text{computed} = 0^\circ 45'
$$

The computed bearing of TY is 36°00′ against the known 36°45′: angular misclosure = +0°45′ (the computed bearing is 45′ less than the known one). It is distributed equally among the 5 angles (+9′ each).

#### Step 3: Adjustment

Total correction = +0°45′ (added to the computed bearing of the last line). It is distributed equally over the 5 observed angles: +0°45′ / 5 = +0°09′ per angle. The correction to a line is +0°09′ multiplied by the number of angles used to reach it.

| Line | Computed FB | Correction | Corrected FB | Corrected BB |
|---|---|---|---|---|
| XP | 148°15′ | 0 | 148°15′ | 328°15′ |
| PQ | 60°45′ | +0°09′ | 60°54′ | 240°54′ |
| QR | 109°15′ | +0°18′ | 109°33′ | 289°33′ |
| RS | 44°30′ | +0°27′ | 44°57′ | 224°57′ |
| ST | 277°15′ | +0°36′ | 277°51′ | 97°51′ |
| TY | 36°00′ | +0°45′ | 36°45′ | 216°45′ |

Check: corrected FB of the last line equals the observed value 36°45′.

**Answer:** angular misclosure = +0°45′. Adjusted bearings: XP 148°15′, PQ 60°54′, QR 109°33′, RS 44°57′, ST 277°51′, TY 36°45′.

## Check yourself

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

1. How is the bearing of the next line found from angle to the right?
   A. Previous bearing - 180° - angle
   B. Previous bearing + angle only
   C. Previous bearing + 360° - angle
   D. Previous bearing + 180° + angle (reduced to 0°-360°)
   Answer: D. FB next = FB previous + 180° + angle to the right; e.g. PQ = 148°15′ + 180° + 92°30′ - 360° = 60°45′. (Key point: Rule for angles to the right)

2. The computed bearing of TY is 36°00′ and the known bearing is 36°45′. What is the misclosure?
   A. +0°45′
   B. -0°45′
   C. +1°30′
   D. 0°
   Answer: A. Misclosure = known - computed = 36°45′ - 36°00′ = +0°45′. (Key point: Misclosure)

3. How is the 0°45′ misclosure distributed?
   A. +15′ per angle over 3 angles
   B. +9′ per angle, over the 5 observed angles
   C. +45′ to the last angle only
   D. +7.5′ per angle over 6 angles
   Answer: B. Five angles (P, Q, R, S, T) were observed, so 45′/5 = 9′ each. (Key point: Correction per angle)

4. What correction is applied to the line ST, reached after four angles?
   A. +0°09′
   B. +0°27′
   C. +0°36′
   D. +0°45′
   Answer: C. Line correction = 9′ x number of angles used; ST uses P, Q, R, S, so 36′ and ST = 277°51′. (Key point: Cumulative correction)

## Related in Surveying I

- [Angle misclosure, closed link traverse AT1-ET2](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-link-traverse-at1-et2) — Surveying I, chapter 4
- [Angular misclosure, link traverse ABCDEFG](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-initial-154-50-last-335-30) — Surveying I, chapter 4
- [Corrected bearings, closed link traverse T1-T2](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-link-traverse-t1-t2-corrected-bearings) — Surveying I, chapter 4
- [Link traverse ABCDEF, right turn angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-right-turn-angles-22-17) — Surveying I, chapter 4, asked 3×
- [Adjusted angles and bearings, angles to the left](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aadjusted-angles-bearings-left-angles-aw-dx) — Surveying I, chapter 4
- [Link traverse PABCQ: permissible misclosure](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-pabcq-permissible-misclosure) — Surveying I, chapter 4

## Related in other subjects

- [Closed loop/link traverse, misclosure terms](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-loop-link-traverse-misclosure) — Surveying II, chapter 1
- [Closed loop/link traverse, misclosure balancing](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-loop-link-traverse-angular-misclosure) — Surveying II, chapter 1
- [Closed traverse missing EA bearing, BC length](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcdea-missing-ea-bc) — Surveying II, chapter 1
- [Adjust traverse A-X to E-Y bearings](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-adjust-latitude-departure-ax-ey) — Surveying II, chapter 1