The following bearings were taken in a closed compass traverse.  

Line	Fore bearing	Back bearing
AB	80° 10'	259° 0'
BC	120° 20'	301° 50'
CD	170° 50'	350° 50'
DE	230° 10'	49° 30'
EA	310° 20'	130° 15'

Calculate the corrected fore bearing of line ‘DE’ by assuming that the observed bearing of line ‘CD’ is correct.  

Explanation:

• Fore-bearing (FB) is the direction of a line measured in the forward direction from a known point. The angle between the survey line and the north direction is measured clockwise.
• Back-bearing (BB) is the direction of the same line but measured in the reverse or backward direction from the endpoint back to the starting point. It is in the opposite direction to the fore-bearing and is measured in the opposite direction (180 degrees different).
• Relation between FB and BB:

BB = FB + 180°, if FB < 180°

BB = FB – 180°, if FB > 180°.​

Here there is no local attraction given, so we have to solve by the include-angle method.

Include angle: The horizontal angle measured between two consecutive survey lines or directions.

Include angle = Fore-bearing of next line - Backbearing of previous

The sum of Include angle in clockwise direction (i.e, excluded angle) = (2n+4)90 = (2x5+4)x90° = 1260°

So, the error = 1260°25' - 1260° = 25' 

So, Corrected include angle D = 239°20' - (25'/5') = 239°15' 

Thus, Include angle D = FB_DE - BB_CD 

FBDE = Include angle D +BBCD = 239°15' - 350°50' = 590°05' (- 360°) = 230°5'