Directed angle

A directed angle records the rotation from one ray to another, distinguishing clockwise from counterclockwise motion and often assigning a sign.

Ray (geometry): A part of a line that begins at one point and extends infinitely in one direction. A directed angle starts with one ray and ends with another.
Angle addition: The operation of combining successive angle rotations by adding their measures. Successive directed turns combine by adding signed angle measures.
Inscribed angle theorem: A circle theorem stating that an inscribed angle measures half its intercepted arc. Directed-angle forms handle cyclic configurations without separate cases for intersecting lines.
Undirected angle: An angle measure that records magnitude without distinguishing clockwise from counterclockwise rotation. It discards the orientation that distinguishes a directed angle's two senses.
Angle: A geometric figure formed by two rays sharing a common endpoint, or the amount of rotation between them. Directed angles extend ordinary angle measure by distinguishing rotational direction.
Coterminal angles: Angles that share the same initial and terminal sides but differ by whole turns. A directed angle's ray pair determines its measure only modulo a full turn unless turns are tracked.
Cross ratio: A projective invariant of four points on a line or circle, formed from ratios of distances or coordinates. Directed angles help express the cross ratio of four concyclic points through angle relations.
Signed angle: An angle measure whose sign indicates the direction of rotation under a chosen convention. Some directed-angle conventions attach a positive or negative sign to each turn.
Orientation (mathematics): A consistent choice of direction around a space, such as counterclockwise rather than clockwise in the plane. Orientation determines which sense of rotation counts as positive.
Principal value: A selected representative from an equivalence class of values, chosen within a specified interval. A principal-angle convention selects one standard value for a rotation.

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