You need to find the azimuth in the southeast quadrant, hence, you need to subtract the bearing from `180^o` such that:

`180^o - 40^o 26' 00'' = 139^o 33' 00''`

You need to find the azimuth in the northwest quadrant, hence, you need to subtract the bearing from `360^o` such that:

`360^o - 25^o 30' 00'' = 334^o 29' 00''`

You need to find the angle between azimuths such that:

`334^o 29' 00'' - 139^o 33' 00'' = 334^o 29' 00'' - 139^o 26' 00'' = 195^o 03' 00''`

**Hence, evaluating the angle between `N 25^o 30' 00'' W` and `S 40^o 26' 00'' E` , using the difference between two azimuths, yields `195^o 03' 00''.` **

Simplest answer:

You have the SW sector: 90°

+ the NW sector 90 - (25° 30') = 64° 30'

+ the SE sector = 40° 26'

= Total 194° 56'

If you need to use Azimuths you will get the same answer:

360° - (25° 30') = (359° 60') - (25° 30') = 334° 30'

180° - (40° 26') = (179° 60') - (40° 26') = 139° 34'

and finally

(334° 30') - (139° 34') = (333° 90') - (139° 34') = 194° 56'