How many more angles does a trapezoid have than a triangle?

A trapezoid can have 2 obtuse angles at most, because a trapezoid has two pairs of supplementary angles.

Both supplementary angles cannot be obtuse at the same time.

One has to be acute.

Because it contains a set of parallel lines, the angle pairs at each end of the trapezoid must be complementary, or have a sum of 180 degrees. If one is a 90-degree angle, its neighbor must also be a right angle, and that end of the trapezoid may resemble a rectangle. To remain within the definition of a trapezoid, then, the two remaining angles must not have 90 degrees. Thus, a trapezoid may have a pair of right angles, but cannot have more.