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A position angle (sometimes abbreviated PA) indicates a direction across the celestial sphere. It is analogous to compass points regarding directions on Earth (such as east-northeast), but indicates directions across the sky. The position angle of a direction through a particular point on the celestial sphere is the angle between that direction and a great circle through the point and the celestial north pole.
For example, given a star ("A") and a second star ("X"), the position angle of X in relation to A is the angle with vertex at A, between a line across the sky from A to X and such a line from A to the celestial north pole. Knowing that angle, and having spotted A, you know in which direction across the sky from A to search for X. The angle is conventionally taken such that the range 0-180° represents directions eastward of the celestial north pole.
A position angle can be used to describe the direction of proper motion of a star. It can also be used to help describe the position of an object based upon the position of another (known/recognizable) object. For example, guide stars are stars whose exact position has been measured and recorded, for use in confirming which part of the celestial sphere you are looking at, such as to adjust and correct the aim of your telescope/instrument. Catalogs of guide stars such as the Guide Star Catalog, have been assembled for this exact purpose. To attempt to observe something more obscure, its position might be given in terms of a position angle from a guide star, plus an angular distance from the guide star.