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making edges touch when one object is rotated

Is there any easy way to make two edges touch exactly when one object is rotated? In the picture below, I'm trying to make the two edges of the red solids touch perfectly, at a kind of hinge joint. I've tried resetting the workspace to various planes. I can move the object into place but not align it perfectly.

Alternatively, can I rotate an object around an edge? Hmm, perhaps dupe the object so that there are two copies side by side, group them, rotate, and then delete the dupe. But maybe there's an easier way.

 

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