Abstract: A layout tool and a means for using the tool to fabricate multi-segment elbows and offset joints from rectangular cross-section fibrous air ductboard material. The tool has a triangular main body having at least one structural feature that defines a plane. At least one flange is connected to the main body, is oriented substantially perpendicular to the main body plane, and forms the first side of the triangle. The main body includes a first outer straight edge extending at an angle of 67.50 degrees from the flange forming the second side of the triangle. A second outer straight edge extending at an angle of 78.75 degrees from the flange forms the third side of the triangle. An inner structure of the main body forms a straight edge perpendicular to the plane of the flange. The outer angled and interior straight edges enable 22.5- and 45-degree miter joints to be easily marked and cut in pre-formed fibrous air duct.