Can a quadrilateral have 4 obese angles.

No a quadrilateral can not have obtuse  angles because the angle measurement has to equal 360

Well, first of all, if we’re talking about angles, then they can be "obtuse"
angles, but they can’t be obese angles.  

An obtuse angle is one that’s bigger then 90° but smaller than 180°.

A quadrilateral can have as many as 3 obtuse angles. But not 4, because
all 4 angles have to add up to 360 degrees.

So they could be like  91°,  91°,  91°, and  87° (3 obtuse angles),
or  175°,  100°,  80°, and  5° (2 obtuse angles).

!  Just wanted to point out a quick issue with your response.  While triangles cannot have four obtuse angles, they can have one to three!  For example, it is possible for a quadrilateral to have three angles measuring 100 degrees and one measuring 60.  Otherwise, your answer is correct.   for your