![]() Two angles that share terminal sides, but differ in size by an integer multiple of a turn, are called coterminal angles.An angle is defined by its measure and is not dependent upon the lengths of the sides of the angle (e.g. ![]() the same magnitude) are said to be equal or congruent. Angles that have the same measure (i.e.The names, intervals, and measuring units are shown in the table below: An angle that is not a multiple of a right angle is called an oblique angle.An angle equal to 1 turn (360° or 2 π radians) is called a full angle, complete angle, round angle or perigon.An angle larger than a straight angle but less than 1 turn (between 180° and 360°) is called a reflex angle.An angle equal to 1 / 2 turn (180° or π radians) is called a straight angle.An angle larger than a right angle and smaller than a straight angle (between 90° and 180°) is called an obtuse angle ("obtuse" meaning "blunt").Two lines that form a right angle are said to be normal, orthogonal, or perpendicular. An angle equal to 1 / 4 turn (90° or π / 2 radians) is called a right angle.An angle smaller than a right angle (less than 90°) is called an acute angle ("acute" meaning " sharp").An angle equal to 0° or not turned is called a zero angle.There is some common terminology for angles, whose measure is always non-negative (see § Signed angles): ![]() For the cinematographic technique, see Dutch angle. Otherwise, a convention may be adopted so that ∠BAC always refers to the anticlockwise (positive) angle from B to C, and ∠CAB the anticlockwise (positive) angle from C to B. However, in many geometrical situations, it is obvious from context that the positive angle less than or equal to 180 degrees is meant, in which case no ambiguity arises. Potentially, an angle denoted as, say, ∠BAC, might refer to any of four angles: the clockwise angle from B to C, the anticlockwise angle from B to C, the clockwise angle from C to B, or the anticlockwise angle from C to B, 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 its vertex (in this case "angle A"). For example, the angle with vertex A formed by the rays AB and AC (that is, the lines from point A to points B and C) is denoted ∠BAC or B A C ^. In geometric figures, angles may also be identified by the three points that define them. 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 was used by Eudemus, who regarded an angle as a deviation from a straight line the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines Euclid adopted the third concept. According to Proclus, an angle must be either a quality or a quantity, or a relationship. ![]() Įuclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. Both are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow". The word angle comes from the Latin word angulus code: lat promoted to code: la, meaning "corner" cognate words are the Greek ἀγκύλος ( ankylοs), meaning "crooked, curved", and the English word " ankle". 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. This measure is conventionally defined as the ratio of the length of a circular arc to its radius, and may be signed. 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.Īngle is also used to refer to the measure of an angle or of an angle of rotation. Angles are also formed by the intersection of two planes. ![]() Īngles formed by two rays 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. A green angle formed by two red rays on the Cartesian coordinate system ![]()
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