Question

Can a trapezoid have four obtuse angles

Answer 1

No. A trapezoid has two acute, and two obtuse angles.

Answer 2

The four angles inside EVERY four-sided figure add up to 360 degrees, no matter what the shape of the figure is.

"Four obtuse angles" means "four angles of more than 90 degrees each".

(four times more-than-90) = more than 360

so NO 4-sided figure can have four obtuse angles inside it.