The tape overlays the measurement information on top of the lines and handles. Sometimes this can come in the way of measurement. You can easily turn this off with keyboard shortcuts.
A: toggle angle information
I: toggle distance information
When measuring smaller distances, the overlay information can come in the way. To make it easier to measure such distances, it is best to turn off all overlays and instead use the Tape Inspector.
The inspector gives you all the information you need, at one place. The handles can be used to align with the screen element and the measurement can be read off the inspector.
I to toggle the inspector.
As you switch between shapes, the inspector updates to show you relevant information for that shape.