Position angle a hypothetical binary star with a PA of 135 degrees, that means an imaginary line in the eyepiece drawn from the north celestial pole to the primary (P) would be offset from the secondary (S) such that the NCP-P-S angle would be 135 degrees. When graphing visual binary orbits, the NCP line is traditionally drawn downward—that is, with north at bottom—and PA is measured counterclockwise. Also the direction of the proper motion can for example be given by its position angle. The definition of position angle is also applied to extended objects like galaxies, where it refers to the angle
Angle trisection angles can be trisected. For example, for any constructible angle , an angle of measure can be trivially trisected by ignoring the given angle and directly constructing an angle of measure . There are angles that are not constructible but are trisectible (despite the one-third angle itself being non-constructible). For example, is such an angle: five angles of measure combine to make an angle of measure , which is a full circle plus the desired . For a positive integer , an angle of measure is "trisectible" if and only if does not divide . In contrast, is "constructible" if