Rough framing and trim work often require you to cut unknown angles. Either through trial and error or by a more objective method, unknown angles can become known. Trial and error works well if you have an idea of what the angle is, but if not, you will weary yourself with trips to the saw. Carpenters have a few tricks up their sleeves to help find the dreaded unknown angle.
Trial and Error Method
If you are somewhat familiar with the angle, divide it by two and set your saw to that angle. Cut that angle on two scrap pieces of wood and hold them in place. Notice where the gap is and adjust your saw accordingly. Cut both pieces at the new angle and check it again. Repeat this process until you have a good fit.
When installing widow casing on a triangular widow, the angle could be determined by first setting one piece of casing cut a few inches long against the window jamb, and then overlapping the next piece and marking the intersection points on the inside and the outside of the casing. Draw a line from one point to the other, and use a speed square to measure the angle. Place the square stop against the edge of the casing and rotate the square until your pencil line and the square are aligned. The angle of the cut is where the degree markings along the outside edge of the speed square meet the edge of the casing.
Bevel Gauge Method
A bevel gauge is a great option when you already have a board with the angle you want or where a bevel gauge can be placed in a manner that allows you set to the overall angle. To match an angle of an existing board, loosen the blade on the bevel gauge, place the bevel gauge against the board and tighten the blade when it fits the angle. With the bevel gauge set, transfer the line to the new piece of wood and cut it. Check the cut with the bevel gauge. When you only know the overall angle, set the bevel gauge to fit the inside or outside of the angle. Transfer this angle to the board and divide it in two. Cut the angle on two scraps, and when the two scraps form to fit the overall angle, you are ready to cut your material.