0 degrees
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For the sides to overlap, the angle must be so wide as to double back over itself. Thus, it must be 360 degrees or greater.
-- an angle that measures 90 degrees -- an angle whose sides are mutually perpendicular
It would not have sides because it would be a straight line. A straight angle is 180 degrees. Anything above that is a "Reflex"
The angle can have any value in the range [0, 360) degrees.
An inscribed angle is an angle whose vertex is on the circle and whose sides are chords.