Tricky object to rotate

I am trying to simulate how a lid would open and close and am finding it very difficult to get it to rotate/close correctly so that it meets the resting surface property.

Can anyone please give me advice on this? If needed, I have attached the file.

Thanks.

Bookcase Demo.skp (185.0 KB)

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Thank you for the quick reply. The demonstration is good, although it misses the steps you took to get it flat. Could you please include that so I know how to rotate with precision to flat?

I just rotated it back down the same way.

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Thank you, that’s brilliant.