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Formulas to compute its dihedral angles from the edge lengths and the angle between two adjacent edges were derived for work on the properties of molecules such as cyclobutane that contain a "puckered" ring of four atoms. [55] Historically the term gauche quadrilateral was also used to mean a skew quadrilateral. [56]
In geometry, a Lambert quadrilateral (also known as Ibn al-Haytham–Lambert quadrilateral), [1] [2] is a quadrilateral in which three of its angles are right angles. Historically, the fourth angle of a Lambert quadrilateral was of considerable interest since if it could be shown to be a right angle, then the Euclidean parallel postulate could ...
The 30°–60°–90° triangle is the only right triangle whose angles are in an arithmetic progression. The proof of this fact is simple and follows on from the fact that if α, α + δ, α + 2δ are the angles in the progression then the sum of the angles 3α + 3δ = 180°. After dividing by 3, the angle α + δ must be 60°. The right angle ...
An angle equal to 1 / 4 turn (90° or π / 2 radians) is called a right angle. Two lines that form a right angle are said to be normal, orthogonal, or perpendicular. [12] An angle larger than a right angle and smaller than a straight angle (between 90° and 180°) is called an obtuse angle [11] ("obtuse" meaning "blunt").
An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem. [34]
In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint.
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