SFGate

feeny I am not an expert, but my impression is that they can make custom blinds in shapes you wouldn't believe possible:

The Seventh Element Design Group Hi there,
I would recommend to put roman blinds with blackout backing either inside (within the window frame) or outside(wall or ceiling), special hardware needs to be used in order to make the blinds to go up and down( because of the angle). Depending on the style of the room (contemporary or traditional) I would also put stationary drapery panels and valance (can get be very creative here) to make the room look prettier.

Brittany Jackson I have a feeling that custum blinds like that picture would cost me a fortune. I like the idea of roman blinds, I could probably figure something out with those. Trying to imagine how a valance would work . . .

kristaldewitt I think putting a valance up would have issues for you also. I feel it might have to be to long to have that straight valance line which would then looked off balanced.

Brittany Jackson What about a custom angled valance that follows the line of the ceiling? I could make of of those myself pretty easily the only problem is I'm not sure how to get the curtains to hang properly. I can't put them on a rod because they'll slide down to one side and I want them to be able to open and close . . . There's a picture on houzz that has fabric just tied in a knot over a knob but you wouldn't be able to open and close them. They could be pulled to the side I guess and the valance would hide the knobs if it looked to funny.

pollyannagal Roman blinds would be the simplest solution for these windows and would not be too tricky - basically the top section of a roman blind is fixed to a batten and can be any shape as it only serves to cover the cords. All the functionality is in the cords at the back of the blind and they will just be of varying lengths to suit the angle. You would effectively have a triangle at the top that doesn't pull up with the straight blind below. If you are planning on making them yourself and want more details I could draw a sketch for you, otherwise speak to a local seamstress about what you want. The downside of this solution is that you would have the top section of the windows covered when the blinds are open so it will reduce the amount of light in your room and will hide the shape of the windows (although this would still be reflected in the shape of the blind).

If you want to show the shape of the windows, maximise light in the day and be able to blackout for sleep then plantation shutters as Feeny suggested would be ideal. This would cost more than roman blinds but your windows are not too difficult a shape so it shouldn't be too scary. I have no idea of prices in the USA but prices here in the UK have come down a lot in recent years as they have become more popular so if you like the look it is worth getting quotes.

I often wonder if architects ever think about the practicality of dressing windows when they design them, or if they are just lucky enough not too need a darkened room to sleep!