holding option and dragging from the end of the measure tool is supposed to create an angle measure or protractor, but it just clears the measurement. version 21.0.0 on Catalina 10.15.1
I am experiencing this on Windows as well. (Windows 10, Photoshop 21.0.0)
The angle measurement appears to be functional and accurate (if you look at the numeric angle display, it does indeed change), but the second segment (that should be created after Option/Alt-clicking on the end point) is invisible.
Using the ruler tool in Photoshop v21.0.1 does not allow the measurement of angles.
Select the ruler tool and drag out a line. Hold the Alt key and drag out a second line from the first This should display both lines and the angle between them should be readable in the options bar:
CC2018 works correctly
CC2019 the first line vanishes but the points remain and the angle is displayed
CC2020 (v21.0.1) both lines disappear when attempting to drag out the second line
System : Windows 10 v1903 build 18362.476 GPU NVidia GTX1080 driver v 436.15
The behavior you describe across the last 3 versions is consistent with my experiences as well, on MacOS 10.13.
I do, however get the angle and length readings in the info panel, and it's only the lines that are invisible. Still, that makes fine measurements unreliable enough that I'll concur that the tool, barely functional in 20.x, is broken in 21.x.
There is a temporary workaround for this problem. Load an image of a protractor onto a layer, making sure it is transparent. You can then move it with the transform controls found in the moVe tool or by pressing ctrl t. Once in the exact place, measure and mark a different layer where you want. Hide the protractor layer.
You can make a ruler in the same manner which can be useful to get an exact line at the length you want as you draw them.