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Included angles can be measured _________.
Clockwise
Counter clockwise
Both A and B
In A or B
In A or B
Included angles in a traverse survey are defined as the interior angles between two successive survey lines. These angles can be measured either clockwise or counter-clockwise from the back station to the forward station, depending on the orientation of the traverse and the instrument settings used by the surveyor.
Included angles in a traverse survey are defined as the interior angles between two successive survey lines. These angles can be measured either clockwise or counter-clockwise from the back station to the forward station, depending on the orientation of the traverse and the instrument settings used by the surveyor.
θincluded=∣α2−α1∣ — where α1,α2 are the bearings of the back and forward lines.
In theodolite surveying, the included angle is typically measured by observing the horizontal circle readings. The surveyor measures the angle at a station by sighting the back station and then the forward station. Because the traverse can be run in a clockwise or counter-clockwise direction, the measured interior angle is simply the difference between the two circle readings, regardless of the direction of rotation.
Included angles are always the interior angles of the polygon formed by the traverse.
For a closed traverse, the sum of interior angles must equal (2n−4)×90°.
The choice of measurement direction (clockwise/counter-clockwise) is a matter of field convenience and does not change the geometric interior angle.
Theodolite traverse stations are usually occupied to measure these angles directly.
Flexibility in field procedure depending on local topography.
Allows direct calculation of interior angles without complex coordinate transformation.
Incorrect orientation leads to measuring exterior angles instead of interior angles.
Requires careful adjustment if the sum deviates from the theoretical geometric sum.
Cadastral surveying for property boundaries.
Control surveys for large infrastructure projects like dams or tunnels.
The term 'Included angle' implies the angle contained inside the traverse polygon.
If the traverse is run in a clockwise direction, the interior angle is measured counter-clockwise from the preceding line, and vice-versa.
D is correct — Included angles can be measured either clockwise or counter-clockwise depending on the surveying convention and the progression of the traverse.
Always verify if the traverse is closed in a clockwise or counter-clockwise direction to determine whether the included angle calculation requires adding or subtracting 360°.