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First, I'm assuming when you say 1:20 you're talking about 1 unit of horizontal run for every 20 units of vertical rise (as opposed to rise over run). If that's the case atan(1/20) = 2º51'45" = 2.86240523º from vertical, which is not the same as 2º87'. Having the right angle will get you a lot closer.
Second, SW considers two points coincident/horizontal/vertical if they are at the same linear position down to 8 digits. However, I don't know how close two lines have to be in angle before they are considered parallel/vertical/horizontal. My guess is the angular difference needs to be less than 8 digits. Either that or the endpoints of the lines need to line up in position. If your angle is 8 digits that means it's value is good to +/- 5e-9. So if your trapezoid is at least 2 units tall, your endpoints will be off by 1e-8 units (s = r * theta, 1e-8 = 2 * 5e-9).
Lastly, what do you mean by "rotate the trapezium"? It sounds like you're trying to apply a 2.87 degree angle to the free rotating trapezoid. This method will be subject to the approximation error mentioned in my second point. If you want a side to be vertical, why don't you just make it vertical via relations? If you want the rotation of the trapezoid to be adjustable, dimension the rotation relative to the angled side instead of the horizontal top or bottom. That way you can just enter a round number like 90deg or 180 deg to make the side vertical. It just seems like you're making things overly complicated.
When you first create your trapezoid, do not use any horizontal or vertical constraints. Constrain the parallel sides with a parallel constraint. Get the trapezoid constrained to a state where you can drag it around but it keeps the same shape.
THEN anchor the shape to a point and constrain one side vertical.
The points I have taken are:-
1) Go back to the drawing board and define slopes with graphical construction.
2) Analyse the consequences of making a relation or constraint.