## 5. Bearings from Deflection Angles

Deflection angles are measured traveling counter-clockwise around a loop traverse. Starting with an bearing of S 18°45'30" W for line JK, determine bearings of the remaining lines.

##### (a) Check angular misclosure.

Since this is a non-crossing loop traverse, the deflection angle sum should be ±360°00'00". Right deflection angles are positive, left are negative.

##### (b) Compute bearings

Depending on bearing quadrants and deflection angle direction, the deflection angle might be added to or subtracted from the previous bearing angle or vice versa to compute the next bearing. While it's possible to set up some rules, it's simpler to draw a sketch to visualize the relationships and computation.

At point K

Line JK's extension through K has the same bearing as line JK.

In this case, the bearing angle is computed by subtracting line JK's bearing from the deflection angle:

Which puts line KL in the SE quadrant:

At point L

From the sketch, it can be seen that the sum of the previous bearing and deflection angles exceed 180° putting line LM in the NW quadrant:

At point M

In this case, the previous bearing angle is subtracted from the deflection angle:

At point N

This one is a little more convoluted because of the lines and angles geometry.

From the sketch:

At point J

Finally, always compute back into the beginning direction as a math check.