However, in many geometrical situations, it is evident from the context that the positive angle less than or equal to 180 degrees is meant, and in these cases, no ambiguity arises. Potentially, an angle denoted as, say, ∠BAC might refer to any of four angles: the clockwise angle from B to C about A, the anticlockwise angle from B to C about A, the clockwise angle from C to B about A, or the anticlockwise angle from C to B about A, where the direction in which the angle is measured determines its sign (see § Signed angles). Where there is no risk of confusion, the angle may sometimes be referred to by a single vertex alone (in this case, 'angle A'). For example, the angle with vertex A formed by the rays AB and AC (that is, the half-lines from point A through points B and C) is denoted ∠BAC or B A C ^.

The three defining points may also identify angles in geometric figures. See the figures in this article for examples. In contexts where this is not confusing, an angle may be denoted by the upper case Roman letter denoting its vertex. Lower case Roman letters ( a, b, c, . . . ) are also used. In mathematical expressions, it is common to use Greek letters ( α, β, γ, θ, φ, . . . ) as variables denoting the size of some angle (to avoid confusion with its other meaning, the symbol π is typically not used for this purpose). The first concept, angle as quality, was used by Eudemus of Rhodes, who regarded an angle as a deviation from a straight line the second, angle as quality, by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines Euclid adopted the third: angle as a relationship. According to the Neoplatonic metaphysician Proclus, an angle must be either a quality, a quantity, or a relationship.

The word angle comes from the Latin word angulus, meaning 'corner.' Cognate words include the Greek ἀγκύλος ( ankylοs) meaning 'crooked, curved' and the English word ' ankle.' Both are connected with the Proto-Indo-European root *ank-, meaning 'to bend' or 'bow.' Įuclid defines a plane angle as the inclination to each other, in a plane, of two lines that meet each other and do not lie straight with respect to each other. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. Angle of rotation is a measure conventionally defined as the ratio of a circular arc length to its radius, and may be a negative number. The magnitude of an angle is called an angular measure or simply 'angle'. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection. Angles are also formed by the intersection of two planes these are called dihedral angles. Īngles formed by two rays are also known as plane angles as they lie in the plane that contains the rays. In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. JSTOR ( July 2022) ( Learn how and when to remove this template message)Ī green angle formed by two red rays on the Cartesian coordinate system.

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Central angle geometry definition