The sines of supplementary angles are equal. If a point P is exterior to a circle with center O, and if the tangent lines from P touch the circle at points T and Q, then ∠TPQ and ∠TOQ are supplementary.

For example, adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) are supplementary. However, supplementary angles do not have to be on the same line, and can be separated in space. Such angles are called a linear pair of angles. have a common vertex and share just one side), their non-shared sides form a straight line. If the two supplementary angles are adjacent (i.e.

Two angles that sum to a straight angle ( 1 / 2 turn, 180°, or π radians) are called supplementary angles.

The angles a and b are supplementary angles. 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 ^ (The tangent of an angle equals the cotangent of its complement and its secant equals the cosecant of its complement.) The prefix ' co-' in the names of some trigonometric ratios refers to the word 'complementary'. 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, meaning 'corner' cognate words are the Greek ἀγκύλος (ankylοs), meaning 'crooked, curved,' and the English word ' ankle'.

4.5 Alternative ways of measuring the size of an angle.

Definition of a supplementary angle