Question

Traversing is carried out for a closed traverse PQRS. The internal angles at vertices P, Q, R, and S are measured as 92°, 68°, 123°, and 77°, respectively. If fore bearing of line PQ is 27°, fore bearing of line RS (in degrees, in integer) is \(\underline{\hspace{1cm}}\).

Hint:

To calculate the fore bearing in a traverse, use the sum of the internal angles and adjust for the required direction at each vertex.

Answer 1

Correct Answer: 196

In a closed traverse, the sum of the internal angles is \( (n - 2) \times 180^\circ \), where \( n \) is the number of sides (here \( n = 4 \)). Thus, the sum of the internal angles should be \( 360^\circ \). Now, we can calculate the fore bearing of line RS. First, find the exterior angle at vertex S: \[ \text{Exterior angle} = 180^\circ - 77^\circ = 103^\circ. \] Next, the fore bearing of line RS is calculated as: \[ \text{Fore bearing of RS} = 27^\circ + 92^\circ + 103^\circ = 196^\circ. \] Thus, the fore bearing of line RS is \( \boxed{196^\circ} \).