How to use a protractor if you can't see what you are measuring?
The angle between the ruler part and the the semicircular part is the same as the angle indicated on the scale.  This is because the centreline of the ruler is parallel to its edge.
In more detail:

Image from Wikimedia Commons user Krishnavedala
Consider line a to be the top edge of the ruler in the picture and line b the centreline.  Line t, the transversal, is the base of the semicircle.  The top right θ where a and t meet is the angle you want to measure.  The bottom left θ is the angle the pointer makes with the semicircle.
This is a useful protractor for setting an angle or measuring a physical object with some thickness. For work purely on paper I'd prefer the clear plastic sort, marking in pencil and then using a steel rule for cutting if necessary.
Say you want to measure the interior angle of the parallelogram shown in freehand blue in this picture (imagine it drawn on paper under the ruler).

You align the protractor as shown, so the edges highlighted in thin red  run along the lines you're interested in.  Then the other angle in red is what you read off.  This is a copy of the first red angle, rotated and enlarged (hence thicker), but not distorted.  You can see that this runs through the pivot and point to the pointer, aligned with its groove.