3. Basic Angles from Directions

a. Bearings

(1) Example 1

The bearings of lines TS and SR are S 52°55' W and S 83°20' E, respectively.

What is the angle right at S from T to R?

Start with the given information	Label whet we're determining
Add the back-bearing TS
	a = 180°00'-(52°55'+83°20') = 43°45'

(2) Example 2

The bearing of ZU is S 23°55’07” E; the bearing of UH is N 78°05’00” E.

What is the defelction angle at U from Z to H?

Start with the given information.	Label what we're determining
Add the back-bearing UZ
	d = 180°00'00"-(23°55'07"+78°05'00")    = 77°59'33" A deflection angle must have a suffix to indicate turning direction defl angle = 77°59'33" L

b. Azimuths

(1) Example 1

The azimuths of lines JK and KL are 82°16'55" and  151°48'15", respectively.

What is the angle right at K from J to L?

Start with the given information.	Label what we're determining.
Add the back-azimuth for line KJ
	f = 262°16'55"-151°48'15" = 110°28'40"

(2) Example 2

Azimuth of line WX is 215°35’; azimuth of line XT is 130°50’

What is the deflection angle at X from W to T? 

Start with the given information.	Label what we're determining.
Extend WX through X and add the azimuth of WX
	d = 215°35'-130°50' = 84°45' A defl angle must end with an L or R suffix to indicate turn direction. defl angle = 84°45' L