The following interior angles were measured in a compass closed traverse. The bearing of the line AB was measured 150° 15′ with prismatic compass. Calculate the bearings of all the other lines. If ∠A =209°45′, ∠B= 50°15′,∠C=95°15′,∠D= 102 °15′ and ∠E=82°30′

The following interior angles were measured in a compass closed traverse. The bearing of the line AB was measured 150° 15′ with prismatic compass. Calculate the bearings of all the other lines. If ∠A =209°45′, ∠B= 50°15′,∠C=95°15′,∠D= 102 °15′ and ∠E=82°30′

SOLUTION :

First check for interior angles of a closed traverse

∠ A+∠B+∠C +∠D +∠E

= 209° 45′ +50°15’+95°15′ +102°15’+ 82° 30′

= 540°00′

 

The Sum of interior angle should be ( 2N-4)x 90°[ N= no of angles ]

=( 2×5-4)×90°

=540°00′

F.B Of line AB= 150°15′

interior∠B= 50°15′

F.B of Line BC= F. B of line AB + ∠B – 180°

=150°15’+50°15′-180°

=20°30′

∠C=95°15′

F.B Of line CD = F. B Of line BC + ∠C  – 180°

=20°30’+95°15’+180°

=295°45′

∠D=102°15′

F. B Of Line DE = F. B Of line CD +∠D – 180°

=295°45′ + 102°15′ – 180°

=218°00′

∠E=82°30′

F. B of line EA = F. B Of line DE + ∠E – 180°

=218°00’+82°30′-180°

=120°30°

∠A=209°45′

check:

F. B Of line AB = F. B Of line EA + ∠A – 180°

=120°30’+209°45′-180°

=150°15′