Obtuse means greater than 90 but less that 180 degrees.
The angles in a quadrilateral sum to 360 degrees. There must be 4 angles in a quadrilateral.
take a square: 90 + 90 + 90 + 90 = 360
for all of these angles to be obtuse they'd have to be at least 91 degrees.
91 + 91 + 91 + 91 = 364
Therefore, my answer is no.
Hope this helps :)
