How do you measure a dip angle with a protractor?
The key is that you need some way of knowing which way is down---and for that, we use gravity, using either a level (perpendicular to gravity) or a plumb bob (parallel to gravity).
Once you have clearly determined which way is down, simply use the protractor to measure the angle between the surface that you want the dip angle for and the straight downward direction. Remember that a flat, level surface has zero dip; so the dip is not the angle with the plumb bob, but 90 degrees (`pi/2 ` radians) minus that angle.
In practice, there is a tool called a Brunton compass that contains a compass, a level, and a protractor, which can be directly used to measure dip angles.