While building and trimming staircases, I often run into odd angles that must have mitered trim applied. I find them simply by using a bevel gauge and a piece of stiff paper—no protractor or compass required.
As shown in the drawing, I place the paper along the straight edge of a board. Then I place the body of the bevel gauge, with its blade set at the required angle to be bisected, against the board (1). Next, I cut the paper with a utility knife guided by the bevel gauge’s blade (2). To find the angle required for the miter cuts, I fold the sheet of paper in half (3). This action bisects the angle, and the resulting folded piece of paper can be laid on a tablesaw or against a miter saw’s fence to adjust for the cut; no numbers need be involved.
John Smyth, St. John’s, None
Edited and Illustrated by Charles Miller
From Fine Homebuilding #185
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Good. This is a simple method. It can also be done with a compass, but that method is a bit more involved.
Not only is this a great tip, it even has all the illustrations so it's clear how it's done. Sort of like the tip itself - no deep calculations necessary.
I use an angle bisector. General used to make a small one.