Example 1: "What's the common measuring unit of the speed of a car in the United States?" Do we say "It's mile per hour" or "It's miles per hour"?
Example 2: "Please enter the degrees of the angle:" as the text for an input field. Is it okay to say "Please enter the degree of the angle" too?
Example 3: "Angle (degrees)". Also a text for an input field. Should we write "Angle (degree)" instead?
This is NOT a question asking whether units are singular or plural following a number. That has been already well answered here.
One of the answers in the link mentioned that "All of the units are inherently plural". If this is true, we should say the unit for speed in the metric system is "meters per hour" instead of "meter per hour". Since this is a single answer and it doesn't have any reference, I'm not sure if it's correct. Even if it's true, why "m/s" then?