A closed traverse constructed after doing a compass survey can be checked for error by a simple formula.
As per the geometry, in a closed traverse with 'n' number of sides the total sum of the interior angles = (2n-4) * 90 degrees.
Example: Consider a pentagon with five sides and five number of interior angles A, B, C, D and E.
Sum of the interior angles = (2*n - 4) *90
= (2*5 - 4) *90
= 540 degrees.
If it was a hexagon, then n= 6
and sum of interior angles would be
= (2*6 - 4)* 90 =720 degrees
Apply this check to the closed traverse at hand and see the error.
Sum of the given interior angles - (2n- 4)*90
Correction = - Error.
Generally the error is equally divided among the interior angles of the traverse. So correction for each angle = - (Error) / n
If the exterior angles are given, then the total sum of the exterior angles = (2n+4)*90
remember an exterior angle = 360- interior angle.
For example exterior angle at A = 360- Int. angle A.
Calculate the Error, E = Total Sum of exterior angle - (2n+4)*90
Correction = -E
Divide the correction equally for each angle = -E/n.