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You need to choose first if you wish to use the large adhesive pad type hangers or the wire frame type.
The *fit of a wire frame plate display hanger to your exact piece in each case is the primary issue... unfortunately each brand of plate hanger fits differently... you will have to inspect a range of options and see what fits your pieces the best.
A large art and hobbies supply store (such as Aaron Brothers Art Mart.. will have a range of decorative plate hanging kits available... these feature hooks that spread around the bottom perimeter of each piece... you will have to inspect the offerings for a proper fit to your particular items.
Use an electric drill and an 1/8" drill bit to drill a hole in the wall from which to hang each plate, drill the hole at an upward angle to the face of the wall, 20 or 30 degree angle, 1 inch deep, then put a finishing nail in the hole and hang each item from that.
CLICK HERE to see a range of adhesive disc type, and wire frame type plate hangers, Walmart, Lowes, Target, and other stores also carry them... it will pay to shop around.
**** The adhesive hangers are not a bad option at all, if the items are flat on the back and clean so that the adhesive disc sticks, the chances of them ever coming off are slim to none.
The wire frame hangers are most often used for very heavy pieces or for antiques that need the entire backs exposed for inspection..for contemporary art, the adhesive discs are a good option.
Let me know what you think, we keep going until you have all of the answers you need.