Most miter cuts will come from joining two pieces of wood together to create a 90-degree angle. For instance, if you are building a picture frame you will have four corners with a perfectly square 90-degree angle. To make each corner requires the creation of two cuts at the precise angle of 45 degrees. To complete your picture frame it will take a total of eight cuts, all made at 45 degrees. However, when one is fitting molding to the inside of a house (especially an old house), they will find that not all corners are square; thus some variation is needed from merely cutting 45-degree angles.
Do your basic math. Cuts used to form a corner in a four-sided room or structure will be made to fill a 90-degree space. Each cut will be 45 degrees. If you have a five-sided room each corner should be at an angle of 72 degrees, so both cuts will be half that amount, or 36 degrees. For a six-sided room the larger angle is 60 degrees and each cut is at 30 degrees.
Make sure each corner is square. This task can be as simple as sliding a framing square into the corner of a room (or around the outside of a corner, if it is an external corner) and seeing if the sides of the square form a tight fit against each wall. If they do, you can go ahead and make your two cuts, but if the corner is out of square, then it is time to revisit your high school geometry class.
Begin the geometric layout in an inside corner by measuring along the side of each wall an equal distance--let's say 10 inches--and making a mark on the floor at this point. Connect these two points with a straight line. Measure the line and make a mark at the halfway point. Connect this point to the exact point where the two walls meet and draw your line between the two points. Your two angles should be equal. At this point you can measure the angle with a framing square or, better yet, lay a board in place and mark the cut from the diagonal line that you made on the floor.
(for an outside corner) Continue the lines of the wall for at least a foot in the direction that goes away from the corner. Do this with both sides and then mark a point on each line that is equidistant from the point of the corner--let's say one foot. Connect the two points and mark the halfway point with a crosshatch. Connect this point to the outside corner and you have your angle.
Use the marking method for any corner that is not 90 degrees. Even if you are working in a newly built, hexagon-shaped building, the marking method is the best way to get the correct angle.