Which of the following statement 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.
- ANeither Statement 1 nor Statement 2 is true.
- BOnly Statement 1 is true.
- CBoth Statements 1 and 2 are true.Correct
- DOnly Statement 2 is true.
Solution
Concept
In the included angle method, the angle between two adjacent lines is measured at each station, either clockwise or counter-clockwise.
Formula
Sum of interior angles = (2n - 4) × 90°
Step-by-step solution
1. Statement 1: Included angles may be measured clockwise or anticlockwise. This is true. 2. Statement 2: If the traverse goes around counter-clockwise and the angles are measured clockwise (from the back station to the forward station), the angles are interior angles. This is true. 3. Both statements are true, so the answer is C.
Explanation
Included angles can be read in either direction at each station. When the survey moves counter-clockwise around the closed traverse, clockwise angles fall inside the figure, so they are interior angles. Hence both statements are correct.
Why the other options are wrong
A: Wrong, because both statements are true. B: Wrong, because Statement 2 is also true. D: Wrong, because Statement 1 is also true.
Shortcut
Progress counter-clockwise plus angles clockwise gives interior angles. Progress clockwise plus angles clockwise gives exterior angles.
Common mistake
Thinking clockwise angles are always interior angles, whatever the direction of progress.
Correct answer: C) Both Statements 1 and 2 are true.