The check for traversing by deflection angle method in a closed traverse of n sides is:
- Athe sum of angles must be equal to (2n - 4)
- Bthe sum of angles must be equal to (2n + 4)
- Cthe sum of angles must be equal to 180°
- Dthe sum of angles must be equal to 360°Correct
Solution
Concept
In a closed traverse, the algebraic sum of deflection angles is always 360°.
Formula
Σ(Right deflections) − Σ(Left deflections) = 360°
Step-by-step solution
1. A deflection angle is the angle between the extended previous line and the next line. 2. In a closed traverse, you go round the full figure once and come back to the start. 3. So the total turning is one full circle. 4. The algebraic sum of deflection angles (right +, left −) = 360°. 5. So the answer is (D).
Explanation
When you walk round a closed traverse and return to the start, your direction turns one full circle. That total turning is 360°. So the algebraic sum of all deflection angles must be 360°.
Why the other options are wrong
(A) (2n − 4) right angles is the check for the sum of interior included angles, not deflection angles. (B) (2n + 4) right angles is the check for the sum of exterior included angles. (C) 180° is the sum of the interior angles of a triangle only, not a general check.
Shortcut
Deflection angles = 360°. Interior = (2n − 4)×90°. Exterior = (2n + 4)×90°.
Common mistake
Students confuse the deflection angle check with the interior (2n − 4) or exterior (2n + 4) right angle checks.
Correct answer: D) the sum of angles must be equal to 360°