If you have a bearing of N 15 degrees W, what is your azimuth?

Azimuths are the easiest to deal with because they turn clockwise right around the 'clock' with North being at 12. But, N15W is 15 degrees left of North. That means the azimuth would be 360-15=345 degrees.

Say they asked for S15W. Then, the azimuth would be 180+15=195 degrees.

Azimuths are used in surveying.

At least, that is what I used all the time when I done it.

It is easier and less confusing than messing around with quadrants.

When one has a transit set up, it would be difficult to deal with something like
S40W. Instead, the transit is turned 220 degrees.

The usual bearings are OK when drawing up a deed, but in the field azimuths are easiest.

One just turns an angle right around the 'clock'