When I close my left eye while lying down, why do objects seem to be at a different angle?

It is normal, and has to do with depth perception I believe. Both eyes work together to figure out where things are. If you close one eye, you’ve only got half the information your brain is used to getting.

It’s also called binocular vision; here’s what happens when you shut one eye.

http://www.reframingphotography.com/sites/default/files/user/web_2_binocular_vision.jpg

The other eye is at a different angle from the other because they are in different places in your skull. When both are open AND they are focused, your brain has one of them be dominant (creating an image based mainly on the perspective of one, with input from the other).

You can also demonstrate this to yourself by having both eyes open, and pressing lightly on the side of one eyeball to get them not to point the same way – you’ll see two images, one tilting off focus from the other! Let go, and watch them slide back together and become one 3D view.

To follow up what @Zaku says, your left eye is likely to be your less dominant eye. Most of the information to your brain comes from the dominant eye. Mostly you look at things head on and therefore the difference between the two eyes is not so noticeable. But in your example the angle is quite extreme so the difference is more noticeable.

If you were to take up archery you would need to know which eye is dominant as this determines the side you turn towards the target. For most right handed people it’s the right eye but not always; sometimes the opposite eye to your handedness is dominant.

The word everyone is looking for is parallax

OK now try covering your right eye while looking at an object. Do you get the same effect as you did when you cover your left eye?

When I cover my right eye the image does not change at all because I’m left eye dominate. Most of the time I look exclusively through my left eye but for looking long distances I use my right eye.

The answers above explain it. When I was little I remember we did an exercise where we hold out our hands in front of us and stick out our forefingers and make them meet tip to tip. Then try to do it with only one eye open. When I was little I would miss my fingers from meeting. Now, I have very little shift in view from one eye closed to the other and I don’t miss. I’m not sure why it changed. Maybe my astigmatism? Not sure.