A trapezoid is a quadrilateral. The sum of the interior angles of a quadrilateral is 360°. Four angles whose measure is greater than 90° will sum to a number that is greater than 360°. So, no quadrilateral (including a trapezoid) can have four obtuse angles.
No that would be impossible.Since it is a quadrilateral, the sum of the angles must equal 360 degrees. To be considered obtuse, an angle must be greater than 90 degrees.
A trapezoid is a quadrilateral with two parallel sides.
Depending upon whether you're dealing with an Euclidean geometry, would dictate whether your scenario were possible. In flat-surface, or Euclidean geometry, the sum of the four angles in a trapezoid are 360. In non-flat-surface, or non-Euclidean geometry, you have curved space, upon which interesting angular relationships show up. And it would have to be in a non-Euclidean situation for there to be more than two obtuse angles in a trapezoid.
You are likely not taking a non-Euclidean geometry class. So, for you, the answer would be: No.
