A square
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A polygon with 4 sides has 4 angles. All polyhedra have at least 4 vertices so I cannot think of any shape that meets the requirements.
A regular polygon of n sides (where n > 4) has n obtuse angles. Since there is no limit to the number of sides that a polygon can have, there can be no limit to the number of obtuse angles in a shape.
An irregular polygon with 5 or more sides.
Any irregular polygon with more than three sides can have.
Any polygon with more than 5 sides can do that.