Set square 30-60-90 degree angles. Combining the two forms by placing the hypotenuses together will also yield 15° and 75° angles. They are often purchased in packs with protractors and compasses. Less commonly found is the adjustable set square. Here, the body of the object is cut in half and rejoined with a hinge marked with angles. Adjustment to the marked angle will produce any desired angle up to a maximum of 180°. In many European countries, the most common form of set square combines a 90-45-45 triangle with a protractor into a single tool made of clear plastic. Named "Geodreieck" (German
Angular defect to less than 360°, on a spherical triangle the interior angles always add up to more than 180° (the exterior angles add up to "less" than 360°), and the angles in a hyperbolic triangle always add up to less than 180° (the exterior angles add up to "more" than 360°). In modern terms, the defect at a vertex or over a triangle (with a minus) is precisely the curvature at that point or the total (integrated) over the triangle, as established by the Gauss–Bonnet theorem. For a polyhedron, the defect at a vertex equals 2π minus the sum of all