Closed traverse in this post we will explain you closed traverse and its formulas with example .

What is Closed traverse ?

To end point of such traverse lie at the same place . The sum of internal and external angles of closed traverse are calculated by the following formula.

Formula of closed traverse

sum of interior angles    = (2n – 4) .900
Sum of exterior angles  = (2n + 4) .900
Where is he number of sides of the traverse
For example, if the traverse has six sides then sum of its angles is calculated by putting n=6 as
Sum of interior angles   (2n-4).900
                                     = (2*6-4).900
                                    =   8*900
                                     =    720
Sum of exterior angles    = (2n + 4) .900
                                           =(2 * 6 + 4) .900
                                               = 16 * 900
                                                  = 14400

In example I m using Greater sign (<) instead of Angle sign (<) because in MS word or other texting program have not math’s  signs
That is Angle sign (<)

Example ;-
The bearing of line AB of a  closed traverse ABCDEA is 2110 18’ 40 “ and the following included angles will observed . determine bearings of other lines .
 <A = 92 – 50’ – 20 “ ,  <B = 1090 – 55’ – 40”
<C = 940 – 38’ – 50” , <D = 1250 – 40’ – 40” ,
 <E = 1160 – 54’ – 30”

Solution ;-
For bearing of line AB            = 2440 – 18’ – 40’’
Adding <B                              =1090 – 55’ – 40’’
Total                                      = 3210 – 14’ – 20’’
Subtract                                 =1800 – 00’ – 00”
Fore Bearing of line BC        = 1410 – 14’ – 20’’
Adding  <C                           = 940 – 38’ – 50’’
Total                                    = 2350 – 53’ – 10’’
Subtracting                          = 1800 – 00’ – 00”
Fore Bearing of line  CD    = 550 – 53’ – 10’’
Adding < D                          = 1250 – 40’ – 40’’
Total                                   = 1810 – 33’ – 50’’
Subtracting                         = 1800 – 00’ – 00”
Fore Bearing of line DE  =   10 – 33’ – 50’’
Adding  <E                            = 1160 – 54’ – 30’’
Total                                      = 1180 – 28’ – 20’’
Subtracting                           = 1800 – 00’ – 00”
Fore Bearing of line EA     = 2980 – 28’ – 20’’
Adding <A                                = 950 – 50’ – 20’’
Total                                       = 3910 – 18’ – 40’’
Subtracting                             = 1800 – 00’ – 00”
Bearing of line AB                 =  2110 – 18’ – 40”

Thus calculated value of the bearing of line AB Is same as give . this verifies the solution .
Note This sign (<) is using for Greater but due to available of angle sign that’s way we are using Greater sign . Greater sing is same looking like Angle sign is given below


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