No, it could not.
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Yes, a quadrilateral just need to have 4 sides. Quad- means 4 and -lateral means sides. To have only one tight angle, it has to be either a right angle with 2 acute angles and 1 obtuse angle OR a right angle with 2 obtuse angle s and 1 acute angle.
How about a kite which is a 4 sided quadrilateral that can have 2 equal opposite obtuse angles
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.
Possibly in the form of an arrowhead providing that its 4 interior angles add up to 360 degrees