How to calculate included angles from bearings?/ Calculating interior angles of anti-clockwise traverse in compass surveying.

 Let us solve an example to understand the calculation procedure of interior angles in a closed traverse.

Eg:

The following bearings were noted down with a compass in an anticlockwise traverse. Calculate the interior angles of a closed traverse.

Line	Fore bearing
AB	112°30 '
BC	27°15'
CD	276° 0'
DE	187°45'
EA	118°30'

 

Following are the 4 points or rules to be known before computing the interior angles.

1. For the anticlockwise traverse,

 Included angle = [fore bearing of next line - back bearing of the previous line.]

2. If a back bearing is ＞180°, deduct 180° from the bearing.

3. If a back bearing is < 180°, add 180° to the bearing.

4. If the value of included angle comes -ve, we have to add 360° to compute the angle in the whole circle bearing system.

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Calculation:

The closed anticlockwise traverse is drawn for the given fore bearings as below.

For the anticlockwise traverse,

 Included angle = [fore bearing of next line - back bearing of the previous line.]

Here, back bearing is not given, so we have to calculate the back bearing with the help of fore bearings.

Note: 

          BB 👉 short form of back bearing.

          FB 👉 short form of fore bearing.

1. Angle A:

 ∠A = [FB of line AB - BB of  line EA]

As fore bearing of EA < 180°, we have to add 180° to the FB.

BB of line EA 

                     = [118°30' + 180° ]

                     = 298°30'

              ∠A = [112°30' - 298°30']

                    = -186°

In the whole circle bearing system, the angle cannot be -ve. In such cases, we have to add 360° to the -ve angle.

 ∠A = [-186° + 360°]

         = 174°

2.  Angle B:

 ∠B = [FB of line BC - BB of  line AB]

As fore bearing of AB < 180°, we have to add 180° to the FB.

BB of line A B

                     = [112°30' + 180° ]

                     = 292°30'

              ∠B = [27°15' - 292°30']

                     = -265°15'

              ∠B = [-265°15' + 360°]

                     = 94°45'

3. Angle C:

 ∠C = [FB of line CD - BB of  line BC]

As fore bearing of BC < 180°, we have to add 180° to the FB.

BB of line BC 

                     = [27°15' + 180° ]

                     = 207°15'

              ∠C = [276° - 207°15']

                    = 68°45'

4. Angle D:

 ∠D = [FB of line DE - BB of  line CD]

As fore bearing of CD > 180°, we have to deduct 180° from the FB.

BB of line CD 

                     = [276° - 180° ]

                     = 96°

              ∠D = [187°45' - 96°]

                    = 91°45'

5. Angle E:

 ∠E = [FB of line EA - BB of  line DE]

As fore bearing of DE > 180°, we have to deduct 180° from the FB.

BB of line DE 

                     = [187°45' - 180° ]

                     = 7°45'

              ∠E = [118°30' - 7°45']

                    = 110°45'

Go through the article 👇

👀. Calculating RL by rise & fall method.

Check:

The total sum of interior angles

= [∠A +∠B + ∠C +∠D + ∠E]

= [174° + 94°45' + 68°45' + 91°45' + 110°45']

= 540°

The total value of the angle should be equal to [(2n -4) ✕90°], where n= no. of sides.

[(2 ✕ 5 - 4) ✕ 90°] = [6 ✕ 90°] = 540° ✔

Go through the article 👇

👀. Finding bearings from included angles in compass surveying.

Thank you for going through these calculation steps❤. Have a good day 😄.

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