Yes providing the 4 interior angles add up to 360 degrees
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It is simply a quadrilateral - there is no special name for such a quadrilateral.
Yes it can. All you need to form a quadrilateral is four sides. The angles can be any size as long as the add up to 360 degrees.
This result follows from the theorem that the sum of the angles of a triangle is 180 degrees. Drawing a diagonal in the quadrilateral splits it into two triangles and the angles of the triangles together combine to form the angles of the quadrilateral.
A quadrilateral may have all 4 angles different if it is not a square, rectangle, rhombus, rhomboid, rectangular trapezoid, isosceles trapezoid, or parallellogram.
There can be 4 different acute angles in an irregular 4 sided quadrilateral that all add up to 360 degrees.