This is an oddly domestic example of an astronomical principle … or maybe it only seems domestic to me because I keep a bicycle in my living room. But anyway, three very different objects of the same shape — in this case, a silver dollar, a saucer, and a bicycle wheel — will all fit precisely inside the same angle as long as they’re spaced apart by the right distance. Saying “the Moon looks as big as a dinner plate” doesn’t mean anything unless you say how far away that dinner plate is, is the point.
This is one of those basic ideas that can get kind of complicated once you’re a few steps farther along in using telescopes stuck on one little planet and trying to figure out just how big and how far away that twinkling star is over there, or that distant planet passing by far, far overhead.
It’s from the book A New Astronomy For Beginners by David A. Todd, which is filled with lovely black-and-white illustrations, and can be leafed through, electronically, on archive.org.