I'm not sure if any solution holds true for all rectangles, particularly the limit conditions as AB, DC or BC, DA approach zero. Using moments doesn't seem to be the right approach.

My Sunday morning first try is to calculate the center of mass and then do a simple torque calculation around it. But there is a problem with the way the problem is posed.

What are you suspending the sheet from , how is the suspention connected? A steel rod glued to the point won't have any angle regardless of reasonable weight whereas a simple string will.

Perhaps I'm missing the point...

I asked that and was told it's a point thorugh hte lamina at the centre, and the lamina is oriented vertically. Like driving a nial through it and hanging iton the wall, making it a 2D not 3D problem.

Nevermind, I misunderstood.

I asked that and was told it's a point thorugh hte lamina at the centre, and the lamina is oriented vertically. Like driving a nial through it and hanging iton the wall, making it a 2D not 3D problem.

In that case, as you have the center of mass offset from the point of attachment, the sheet will swing just like a pendulum. It will continue to swing unless there is friction of some type. So, my second guess based on the new information is: there is no one angle, its a dynamic system.

What are you trying to give me a headache?
I notice it doesn't say the masses are equal.

Correct. Whether the masses are kg or any other unit the ratio stays the same.
7:4 across the long sides and 6:5 across the short sides.
So it seems solvable by moments without knowing the units.

However the question of whether the angle remains the same at all rectangle sizes bugs me.