No because 4 obtuse angles would be over 360 degrees and the angles of a 4 sided quadrilateral add up to 360 degrees no more and no less.
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Yes. All parallelograms, except their degenerates form (rectangles), must have two obtuse angles.
No, it could not.
Yes a 4 sided quadrilateral can have angles that include obtuse angles providing the that all the 4 interior angles add up to 360 degrees.
A 4 sided quadrilateral can never have 4 obtuse angles.
How about a kite which is a 4 sided quadrilateral that can have 2 equal opposite obtuse angles