The mitre cut is necessary when joining two boards at an angle-- most often when joining the trim around a door or window, the corners of baseboard and moulding or in building a picture frame. For inside and outside base corners, the angles will be 90 degrees, but not always. In order to make the corner you need to cut two pieces of material at a 45-degree angle. When you join them together they make the 90-degree corner. If the corner is not exactly square, you can fix that easily.
Use your protractor to measure the angle of the corner. You must know whether it is smaller or greater than 90 degrees before you start cutting.
Divide the angle by two. You have to make two cuts to equal the entire angle so the finished joint will look attractive. A mitre box will make 45-degree and 90-degree angle cuts.
Transfer the cutting line onto both pieces if you do not have a protractor, overlapping the ends of your two boards so they fit the corner. Mark a line along their intersection from the outer corner to their inner corner with your pencil.You can actually nail them together and cut both pieces at the same time. This will give you a perfect pattern for marking the finished pieces.
Use an adjustable mitre saw if your corner angles are slightly imperfect, adjusting only one of your corner pieces for a snugger fit. Coping mouldings is a more refined than mitring for achieving difficult fits.
Draw a picture of the object you are making to assist in visualising the angles. Double check all of your calculations before you start cutting.
Remember that every bend has two angles. One on each piece making the bend.