Calculation of Included Angles in Compass Traverse|Civil Easy Learning

Calculation of Included Angles of a Traverse in Compass Traverse

When two lines meet at a point two angles i.e., interior and exterior angles
are formed. The sum of these two angles is equal to 360.

 The following rules may be applied to find the included angle between two lines whose bearings are given.

Finding of included angles is divided into two cases as follows:

1. When the W.C.B of two lines measured from their point of intersection
are given
2. When the W.C.B. of two lines not measured from their point of
intersection are given.
Case (1) When the W.C. bearings of two lines measured from their point
of intersection are given

Rule: Subtract the smaller bearing from the greater one. The difference
will give the included angle. If it is less than 180
 However if the difference exceeds 180
 it will be the exterior angle.
The included angle is then 360 – exterior angle

Example:
The bearings of the sides of a closed traverse ABCDE are as follows:

Compute the interior angles of the traverse.
A = Bearing of AE - Bearing of AB
 = B.B. of EA - FB of AB
 = 302 45’ - 105 15’ = 197 30’ = exterior angle
Interior angle A = Angle EAB = 360  – 197 30’ = 162 30’
B = Bearing of BA - Fore Bearing of BC
 = B.B. of AB - FB of BC
 = 285 15’ - 20 00’ = 265 15’ = exterior angle
Interior angle B = Angle ABC = 360  – 265 15’ = 94 45’
C = Bearing of CB difference Bearing of FB of CD
 = B.B. of BC - FB of CD
 = 200 00’ -  229 30’ = 29 30’ = interior angle
D = Bearing of DC - FB of DE
 = B.B. of CD - FB of DE
 = 49 30’’ - 187 15’ = 137 45’ = interior angle
E = Bearing of ED - Fore bearing of EA
= B.B. of DE - FB of EA
 = 7 15’’ - 122 45’ = 115 30’

Check:
The sum of the interior angles of a closed traverse must equal to
(2n-4) right angles, where n is the number of the sides of the traverse. In this
case the sum of the angles must be equal (10-4) x 90 = 540
.
A + B + C + D + E = 162 30’ + 94 45’ + 29 30’ + 137 45’ +
115 30’ = 540 00’. Hence checked.