In my study material, there is a chart of the fundamental units. In that solid angle and angle are separated by a line from the other fundamental units. What is the reason for that?
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My guess that it's to separate them from fundamental physical units. You can think of an angle of 5000 degrees or maybe an angle of 1,000,000 radians, they may be interpreted as rotation of how ever many rotations, but in either case they are not a fundamental (physical) units such as mass, force etc..