A vertex of a quadrilateral can have any measure between (but excluding) 0 degrees and 360 degrees. The only requirement is that the four angles add to 360 degrees.
So a quadrilateral can have angles of 0.1, 0.1, 0.1 and 359.7 degrees.
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A quadrilateral is a shape with four sides... It doesn't have *one* angle. The sum of the interior angles of a quadrilateral will always be 360 degrees, however, it is impossible to know the value an individual angle of a quadrilateral with the information given.
It is just an irregular quadrilateral.
Any angle <360 degrees is possible, though it would be a concave quadrilateral if the angle were greater than 180 deg.
There is no specific limitation on any one angle of an inscribed quadrilateral.
A quadrilateral can have four right angles.