A rain gutter miter is basically a miter joint, where two pieces of something are cut on a 45 degree angle making a 90 degree corner with the two pieces. You not only see miters in gutter systems, you will find them in all types of building, from wood work to other things like tile work or furniture building.
Gutters are sold as seamless gutters in most cases, however, all the corner pieces have seams. Only the long straight pieces of gutter come out in one piece, and there is no way to turn a corner without cutting the ends to make this corner miter.
There are a couple different options with the making of a corner miter. You have some professional gutter installers that can cut the corner miter, and fold the ends to make the corner look like one piece of gutter. Some gutter contractors like me, use miter strips.
Miter strips are designer cut strips that cover the cut corners of the two pieces of gutter from the outside. This makes a nice looking colonial type design corner. This way of doing the miter is a bit easier, being that the installer does not have to be as accurate with their end cuts.
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There are also miter boxes that a person can buy. These are pre made corner pieces that the cut gutters just drop in to making the turn. This is the best way to go if you plan to do a miter corner by yourself for the first time. These pre-made corners are a bit more expensive but over all, way easier to install.
Inside miters are the corners that point inward, and the outside miters, are the ones that point out, for instance when a wall turns a different direction at the corners of the roof.