Q.Determine which of the following pairs of angles are co-terminal.

A directed angle $\angle AOB$ is formed by rotating an initial ray $OA$ about its endpoint $O$ until it reaches a terminal ray $OB$; the rotation's sense (anticlockwise = positive, clockwise = negative) is part of the angle's identity, so $\angle AOB \ne \angle BOA$ in general. Special cases follow directly from how far the ray has turned: a zero angle ($0°$, no rotation), a right angle ($90°$, a quarter turn), a straight angle ($180°$, half a turn) and a one-rotation angle ($360°$, a full turn).

An angle is in standard position when its vertex is at the origin and its initial arm lies along the positive $X$-axis; it is then said to lie in whichever quadrant its terminal ray falls in, or to be a quadrantal angle if the terminal ray falls exactly on an axis. To find the quadrant of an angle outside $0°$–$360°$, reduce it modulo $360°$ first.

Two standard-position angles are co-terminal (share the same terminal ray) exactly when the difference of their measures is an integral multiple of $360°$ -- e.g. $30°, 390°, -330°$ are all co-terminal.