I assume when you say vertical you mean a straight line.
If so, then the answer is NO, two obtuse angles cannot be vertical. Obtuse angles have to be greater than 90 degrees, so the least an obtuse angle can be is 91 degrees.
91 + 91 = 182, and a straight line is 180 degrees.
So two obtuse angles cannot be vertical because even the lowest degrees that two obtuse angles can be is greater than 180 degrees (a straight line).
