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Calculating Internal Angles in a Traverse:

  1. Traverse: A sequence of connected survey lines forming a closed loop.
  2. Interior Angle: The angle formed between two consecutive sides of a traverse.
  3. Clockwise Traverse: The order of points is clockwise.
  4. Counterclockwise Traverse: The order of points is counterclockwise.

Method:

  1. Measure the included angles using a theodolite or compass.
  2. For clockwise traverses:
    • Subtract the smaller bearing from the larger one.
    • If the difference is less than 180°, it’s an interior angle.
    • If the difference exceeds 180°, it’s an exterior angle.
    • If negative, add 360° to get the whole circle bearing.
  3. For counterclockwise traverses:
    • Add the smaller bearing to the larger one.
    • Follow the same rules as above.

Calculating Fore Bearing and Back Bearing:

  1. Fore Bearing (FB): The bearing of a line from the starting point to the ending point.
  2. Back Bearing (BB): The bearing of the same line in the opposite direction.
  3. Whole Circle Bearing System (WCB): Bearings measured clockwise from the north direction (0° to 360°).

Method:

  1. For WCB:
    • BB = FB + 180° if FB < 180°
    • BB = FB - 180° if FB > 180°
  2. For Quadrantal Bearings:
    • BB = Numerically equal to FB (change N for S and E for W).

Sum of Interior Angles in a Polygon:

  1. Regular Polygon: All interior angles are equal.
  2. Irregular Polygon: Interior angles may vary.
  3. Formula:
    • Sum of interior angles = (n - 2) × 180°
    • Where ‘n’ is the number of sides.
    • Examples:
      • Triangle: 180°
      • Quadrilateral: 360°
      • Pentagon: 540°
      • Hexagon: 720°

Remember, the sum of interior angles remains constant regardless of polygon type!

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