A closed -traverse is  conducted in anticlockwise direction with Five stations A, B, C, D, and E in the form of a regular Pentagon. If the F.B Of AB is  45°00′, find the F. B’s of Other sides

A closed -traverse is  conducted in anticlockwise direction with Five stations A, B, C, D, and E in the form of a regular Pentagon. If the F.B Of AB is  45°00′, find the F. B’s of Other sidesA closed -traverse is  conducted in anticlockwise direction with Five stations A, B, C, D, and E in the form of a regular Pentagon. If the F.B Of AB is  45°00′, find the F. B’s of Other side

solution.

interior angle of Pentagon

= (2n-4)×90°/5

=(2×5-4)×90°/5

=108°

F. B of line AB = 45°00′ 

∠B= 108°00′

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

=45°+108°+180°

= 333°00′

∠C = 108°

FB Of line CD = F. B of line BC + ∠C -180°

= 333°+108°-180°

=261°00′

∠D =108°

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

= 261+108°-180°

= 189° 00′

∠ E= 108°

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

= 189°+108°-180°

∠A=108°

check:

F. B line AB= F. B of line EA + ∠A-180°

= 117°+ 108°-180°

= 45°00′