Okay, I don't think the last four digits of your model number are going to matter for the purposes of fixing your Chromebook, so let's proceed under that assumption.
The same sort of problem happened with my granddaughter's Chromebook. I opened it up and found that the hinge had actually broken and had to be replaced. Here's a picture of your hinges and the arrow points to the place where it had broken on my granddaughter's laptop.
[image|3588247]
Only one side was broken, but those arrows show where the major stress point is on those hinges. What happens is that once that hinge breaks, instead of spreading the stress along the entire edge of the display backplate, it concentrates it in the corner where you're seeing it come apart. So I'm pretty sure you're going to have to take it apart to verify the hinge is broken and make sure nothing else is damaged; if the stress has broken the hinge's mounting point then you could end up having to replace the display lid along with the hinge.
However, you won't know until you open it up. Use this guide to remove the LCD so you can get a good view of the hinge and see if it's broken.
[guide|149310|Acer Chromebook Spin 11 R751TN-C5P3 LCD Screen & Digitizer Assembly Replacement - iFixit Repair Guide]
If you find that the hinge is actually broken, then you'll need to continue with the instructions to remove the LCD completely, then switch over to the guide showing how to remove the complete display assembly, which you'll have to do in order to replace the hinge(s).
[guide|149316|Acer Chromebook Spin 11 R751TN-C5P3 Display Assembly Replacement - iFixit Repair Guide]
The instructions pick up at Step 6, so if you've finished the other guide you can start there.
Once you have the display assembly removed with the LCD out, the hinges should be straight-forward to replace just by removing a few screws.
Of course, I see that you've already accepted @jameslacro36296's answer, and that is indeed a valid, if somewhat temporary, fix if you don't want to go to the trouble of fixing it right.