Q1. Which of the following statements for the included angle method is/are true?
Statement 1: Included angles can be measured either clockwise or counter-clockwise.
Statement 2: The measured clockwise angles are interior angles if the direction of progress around the survey is counter-clockwise.
📚 Detailed Explanation: Included Angle Method — Both Statements Are True
The included angle method is one of the fundamental techniques for running a traverse survey. At each station, the surveyor measures the angle between the two survey lines (the incoming and outgoing directions). Understanding how the direction of traverse progress affects whether measured angles are interior or exterior is essential for correctly computing coordinates and areas.
Statement 1 Analysis: Angles Can Be Measured Either Way
Statement 1 is TRUE. In field practice, the surveyor can measure the included angle at any station either clockwise (by rotating the instrument to the right) or counter-clockwise (to the left). Both give valid angle measurements. The measurement direction is typically standardized for a project but is not universally fixed.
Statement 2 Analysis: Clockwise Angles = Interior When Traversing Counter-Clockwise
Statement 2 is TRUE. This is a geometric consequence of how angles relate to the polygon formed by the traverse.
| Direction of Progress Around Traverse | Clockwise Measured Angles Are |
|---|---|
| Counter-clockwise (left-hand progression) | Interior (inside the polygon) |
| Clockwise (right-hand progression) | Exterior (outside the polygon) |
When you progress counter-clockwise around a closed polygon and measure each angle clockwise at each station, you are always looking back and then rotating right toward the next leg. This rotation sweeps through the interior of the polygon, making it an interior angle. The sum of all interior angles of a polygon with n sides = (n − 2) × 180°, which serves as a check.
Why Options A, C, and D Are Wrong
A (Only Statement 2): Statement 1 is also true — angles can be measured in either direction. Restricting measurement to one direction is not a requirement of the included angle method.
C (Neither is true): Both statements are established surveying principles supported by standard textbooks and field practice.
D (Only Statement 1): Statement 2 is also true. The relationship between traverse direction and interior/exterior angle classification is a verified geometric principle.
Key Concepts for Students
- Interior angle check: For a closed traverse of n sides, the theoretical sum of interior angles = (n − 2) × 180°. If the measured sum differs, the angular error is distributed proportionately as a correction.
- Exterior vs interior: If exterior angles are measured (survey progresses clockwise and angles measured clockwise), the sum of exterior angles = (n + 2) × 180° for a convex polygon. Knowing which you measured prevents sign errors in coordinate calculations.
- Field practice: Most modern total stations measure clockwise by default. The surveyor controls traverse direction; selecting counter-clockwise progress ensures directly measured clockwise angles are the interior angles, simplifying traverse computation.