Traverse geometry: what is a deflection angle? Select the definition that correctly relates a traverse deflection angle to the interior (included) angle between two successive lines.

Introduction / Context:Two common angular descriptions in traversing are interior (included) angles and deflection angles. Field notes may be kept in either format depending on method and convenience. Knowing how they relate allows consistent computations of bearings, coordinates, and closures.

Given Data / Assumptions:

• Included angle is measured inside the traverse at a station between the back line and forward line.
• Deflection angle is measured from the prolongation of the back line to the forward line, right or left.
• Angles are in degrees (°).

Concept / Approach:

The deflection angle is the supplement of the included angle when both are measured at the same station: deflection = 180° − included angle. Its sense (right/left) indicates turning direction. This relationship holds whether the included angle is acute or obtuse and is fundamental for converting between angle-keeping conventions during traverse reduction.

Step-by-Step Solution:

Verification / Alternative check:

Check with a right-angle corner: included = 90° → deflection = 90°, consistent. For a straight line: included = 180° → deflection = 0° (no turn).

Why Other Options Are Wrong:

Options A and B restrict magnitudes incorrectly. Option D (360° − included) is unrelated to standard traverse definitions. Option E is false by definition.

Common Pitfalls:

Forgetting to note right/left sign; mixing exterior with included angles leading to incorrect azimuth calculations.

Final Answer:

the difference between the included angle and 180°