166 relations: Alternating series, Angle, Angle trisection, Angles between flats, Angular diameter, Angular distance, Angular velocity, Ankle, Arc (geometry), Area, Argument (complex analysis), Argument of a function, Astrological aspect, Astronomy, Azimuth, Babylonia, Babylonian mathematics, Ballistics, Bearing (navigation), Binary scaling, Bisection, Byte, Cambridge, Carpus of Antioch, Cartesian coordinate system, Celestial coordinate system, Celestial sphere, Centi-, Central angle, Circular sector, Circumference, Clock angle problem, Clock position, Clockwise, Cofunction, Cognate, Collinearity, Compass (drawing tool), Compass-and-straightedge construction, Concave polygon, Concurrent lines, Congruence (geometry), Convex polygon, Curve, Cut-the-Knot, Cyclic quadrilateral, Degree (angle), Dihedral angle, Dimensional analysis, Dot product, ..., Earth, English language, Equator, Equilateral triangle, Eratosthenes, Euclid, Euclid's Elements, Euclidean geometry, Euclidean space, Euclidean vector, Eudemus of Rhodes, Extended side, Exterior angle theorem, Firearm, Francis Dominic Murnaghan (mathematician), Full moon, Geographic coordinate system, Geography, Grade (slope), Gradian, Great circle, Great-circle distance, Greek alphabet, Greek language, Greek mathematics, Gudermannian function, Hilbert space, Horizon, Horizontal coordinate system, Hour angle, Hyperbolic angle, Hyperbolic function, Hyperbolic sector, Inner product space, Inscribed angle, Internal and external angles, International System of Units, Interval (mathematics), Introductio in analysin infinitorum, Irrational rotation, James Jeans, Kilometre, Latin, Latitude, Leonhard Euler, Line (geometry), Linguistics Research Center at UT Austin, Logo (programming language), Longitude, Mathematical constant, Measure (mathematics), Metric tensor, Milliradian, Minute and second of arc, NATO, Nautical mile, Navigation, Negative number, Normal (geometry), North, Orientation (geometry), Orientation (vector space), Orthogonality, Parallelogram, Perpendicular, Phase angle, Pi, Pierre Wantzel, Plane (geometry), Points of the compass, Polygon, Polyhedron, Prefix, Prime meridian (Greenwich), Proclus, Proto-Indo-European language, Protractor, Quadrilateral, Radian, Radius, Rational trigonometry, Relative direction, Revolutions per minute, Riemannian geometry, Right angle, Rotation (mathematics), Rule of thumb, Series (mathematics), Sexagesimal, Simple polygon, Sine, Skew lines, Small-angle approximation, Solid angle, Sphere, Spherical angle, Spherical coordinate system, Spiral, Star, Surface (mathematics), Tangent, Tangent lines to circles, Telescopic sight, Thales of Miletus, Theta, Transversal (geometry), Triangle, Triangulation, Trigonometric functions, Turn (geometry), Two-dimensional space, Unit of measurement, Variable (mathematics), Vertex (geometry), Zenith, 12-hour clock. Expand index (116 more) » « Shrink index
In mathematics, an alternating series is an infinite series of the form with an > 0 for all n.
In plane 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.
Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics.
The concept of angles between lines in the plane and between pairs of two lines, two planes or a line and a plane in space can be generalised to arbitrary dimension.
The angular diameter, angular size, apparent diameter, or apparent size is an angular measurement describing how large a sphere or circle appears from a given point of view.
In mathematics (in particular geometry and trigonometry) and all natural sciences (e.g. astronomy and geophysics), the angular distance (angular separation, apparent distance, or apparent separation) between two point objects, as viewed from a location different from either of these objects, is the angle of length between the two directions originating from the observer and pointing toward these two objects.
In physics, the angular velocity of a particle is the rate at which it rotates around a chosen center point: that is, the time rate of change of its angular displacement relative to the origin.
The ankle, or the talocrural region, is the region where the foot and the leg meet.
In Euclidean geometry, an arc (symbol: ⌒) is a closed segment of a differentiable curve.
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.
In mathematics, the argument is a multi-valued function operating on the nonzero complex numbers.
In mathematics, an argument of a function is a specific input in the function, also known as an independent variable.
In astrology, an aspect is an angle the planets make to each other in the horoscope, also to the ascendant, midheaven, descendant, lower midheaven, and other points of astrological interest.
Astronomy (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.
An azimuth (from the pl. form of the Arabic noun "السَّمْت" as-samt, meaning "the direction") is an angular measurement in a spherical coordinate system.
Babylonia was an ancient Akkadian-speaking state and cultural area based in central-southern Mesopotamia (present-day Iraq).
Babylonian mathematics (also known as Assyro-Babylonian mathematics) was any mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC.
Ballistics is the field of mechanics that deals with the launching, flight, behavior, and effects of projectiles, especially bullets, unguided bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance.
In navigation bearing may refer, depending on the context, to any of: (A) the direction or course of motion itself; (B) the direction of a distant object relative to the current course (or the "change" in course that would be needed to get to that distant object); or (C), the angle away from North of a distant point as observed at the current point.
Binary scaling is a computer programming technique used typically in embedded C, DSP and assembler programs to implement floating point operations by using the native integer arithmetic of the processor.
In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.
The byte is a unit of digital information that most commonly consists of eight bits, representing a binary number.
Cambridge is a university city and the county town of Cambridgeshire, England, on the River Cam approximately north of London.
Carpus of Antioch (Κάρπος) was an ancient Greek mathematician.
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
In astronomy, a celestial coordinate system is a system for specifying positions of celestial objects: satellites, planets, stars, galaxies, and so on.
In astronomy and navigation, the celestial sphere is an abstract sphere with an arbitrarily large radius concentric to Earth.
Centi- (symbol c) is a unit prefix in the metric system denoting a factor of one hundredth.
Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians).
A circular sector or circle sector (symbol: ⌔), is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector.
In geometry, the circumference (from Latin circumferentia, meaning "carrying around") of a circle is the (linear) distance around it.
Clock angle problems are a type of mathematical problem which involve finding the angles between the hands of an analog clock.
A clock position is the relative direction of an object described using the analogy of a 12-hour clock to describe angles and directions.
Two-dimensional rotation can occur in two possible directions.
In mathematics, a function f is cofunction of a function g if f(A).
In linguistics, cognates are words that have a common etymological origin.
In geometry, collinearity of a set of points is the property of their lying on a single line.
A pair of compasses, also known simply as a bow compass, is a technical drawing instrument that can be used for inscribing circles or arcs.
Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.
A simple polygon that is not convex is called concave, non-convex or reentrant.
In geometry, three or more lines in a plane or higher-dimensional space are said to be concurrent if they intersect at a single point.
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
A convex polygon is a simple polygon (not self-intersecting) in which no line segment between two points on the boundary ever goes outside the polygon.
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.
Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.
In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.
A dihedral angle is the angle between two intersecting planes.
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed.
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
Earth is the third planet from the Sun and the only astronomical object known to harbor life.
English is a West Germanic language that was first spoken in early medieval England and is now a global lingua franca.
An equator of a rotating spheroid (such as a planet) is its zeroth circle of latitude (parallel).
In geometry, an equilateral triangle is a triangle in which all three sides are equal.
Eratosthenes of Cyrene (Ἐρατοσθένης ὁ Κυρηναῖος,; –) was a Greek mathematician, geographer, poet, astronomer, and music theorist.
Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".
The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
Eudemus of Rhodes (Εὔδημος) was an ancient Greek philosopher, considered the first historian of science, who lived from c. 370 BC until c. 300 BC.
In plane geometry, an extended side or sideline of a polygon is the line that contains one side of the polygon.
The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
A firearm is a portable gun (a barreled ranged weapon) that inflicts damage on targets by launching one or more projectiles driven by rapidly expanding high-pressure gas produced by exothermic combustion (deflagration) of propellant within an ammunition cartridge.
Francis Dominic Murnaghan (August 4, 1893 – March 24, 1976) was an Irish mathematician, former head of the mathematics department at Johns Hopkins University.
The full moon is the lunar phase when the Moon appears fully illuminated from Earth's perspective.
A geographic coordinate system is a coordinate system used in geography that enables every location on Earth to be specified by a set of numbers, letters or symbols.
Geography (from Greek γεωγραφία, geographia, literally "earth description") is a field of science devoted to the study of the lands, the features, the inhabitants, and the phenomena of Earth.
The grade (also called slope, incline, gradient, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal.
The gradian is a unit of measurement of an angle, equivalent to \frac of a turn, \frac of a degree, or \frac of a radian.
A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere.
The great-circle distance or orthodromic distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior).
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC.
Greek (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean and the Black Sea.
Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.
The Gudermannian function, named after Christoph Gudermann (1798–1852), relates the circular functions and hyperbolic functions without explicitly using complex numbers.
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
The horizon or skyline is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not.
The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane.
In astronomy and celestial navigation, the hour angle is one of the coordinates used in the equatorial coordinate system to give the direction of a point on the celestial sphere.
In mathematics, a hyperbolic angle is a geometric figure that divides a hyperbola. The science of hyperbolic angle parallels the relation of an ordinary angle to a circle. The hyperbolic angle is first defined for a "standard position", and subsequently as a measure of an interval on a branch of a hyperbola. A hyperbolic angle in standard position is the angle at (0, 0) between the ray to (1, 1) and the ray to (x, 1/x) where x > 1. The magnitude of the hyperbolic angle is the area of the corresponding hyperbolic sector which is ln x. Note that unlike circular angle, hyperbolic angle is unbounded, as is the function ln x, a fact related to the unbounded nature of the harmonic series. The hyperbolic angle in standard position is considered to be negative when 0 a > 1 so that (a, b) and (c, d) determine an interval on the hyperbola xy.
In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
A hyperbolic sector is a region of the Cartesian plane bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the rectangular hyperbola xy.
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
In geometry, an inscribed angle is the angle formed in the interior of a circle when two secant lines (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle.
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.
The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement.
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
Introductio in analysin infinitorum (Introduction to the Analysis of the Infinite) is a two-volume work by Leonhard Euler which lays the foundations of mathematical analysis.
In the mathematical theory of dynamical systems, an irrational rotation is a map where θ is an irrational number.
Sir James Hopwood Jeans (11 September 187716 September 1946) was an English physicist, astronomer and mathematician.
The kilometre (International spelling as used by the International Bureau of Weights and Measures; SI symbol: km; or) or kilometer (American spelling) is a unit of length in the metric system, equal to one thousand metres (kilo- being the SI prefix for). It is now the measurement unit used officially for expressing distances between geographical places on land in most of the world; notable exceptions are the United States and the road network of the United Kingdom where the statute mile is the official unit used.
Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.
In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface.
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.
The Linguistics Research Center (LRC) at the University of Texas is a center for computational linguistics research & development directed by Prof.
Logo is an educational programming language, designed in 1967 by Wally Feurzeig, Seymour Papert and Cynthia Solomon.
Longitude, is a geographic coordinate that specifies the east-west position of a point on the Earth's surface.
A mathematical constant is a special number that is "significantly interesting in some way".
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.
A milliradian, often called a mil or mrad, is an SI derived unit for angular measurement which is defined as a thousandth of a radian (0.001 radian).
A minute of arc, arcminute (arcmin), arc minute, or minute arc is a unit of angular measurement equal to of one degree.
The North Atlantic Treaty Organization (NATO; Organisation du Traité de l'Atlantique Nord; OTAN), also called the North Atlantic Alliance, is an intergovernmental military alliance between 29 North American and European countries.
A nautical mile is a unit of measurement defined as exactly.
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.
In mathematics, a negative number is a real number that is less than zero.
In geometry, a normal is an object such as a line or vector that is perpendicular to a given object.
North is one of the four compass points or cardinal directions.
In geometry the orientation, angular position, or attitude of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it occupies.
In mathematics, orientation is a geometric notion that in two dimensions allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left-handed or right-handed.
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.
In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).
In the context of phasors, phase angle refers to the angular component of the complex number representation of the function.
The number is a mathematical constant.
Pierre Laurent Wantzel (5 June 1814 in Paris – 21 May 1848 in Paris) was a French mathematician who proved that several ancient geometric problems were impossible to solve using only compass and straightedge.
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
The points of the compass mark the divisions on a compass, which is primarily divided into four points: north, south, east, and west.
In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
A prefix is an affix which is placed before the stem of a word.
A prime meridian, based at the Royal Observatory, Greenwich, in London, England, was established by Sir George Airy in 1851.
Proclus Lycaeus (8 February 412 – 17 April 485 AD), called the Successor (Greek Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major classical philosophers (see Damascius).
Proto-Indo-European (PIE) is the linguistic reconstruction of the hypothetical common ancestor of the Indo-European languages, the most widely spoken language family in the world.
A protractor is a measuring instrument, typically made of transparent plastic or glass, for measuring angles.
In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices or corners.
The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.
In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.
Rational trigonometry is a proposed reformulation of metrical planar and solid geometries (which includes trigonometry) by Canadian mathematician Norman J. Wildberger, currently an associate professor of mathematics at the University of New South Wales.
The most common relative directions are left, right, forward(s), backward(s), up, and down.
Revolutions per minute (abbreviated rpm, RPM, rev/min, r/min) is the number of turns in one minute.
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point.
In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.
Rotation in mathematics is a concept originating in geometry.
The English phrase rule of thumb refers to a principle with broad application that is not intended to be strictly accurate or reliable for every situation.
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
Sexagesimal (base 60) is a numeral system with sixty as its base.
In geometry a simple polygon is a flat shape consisting of straight, non-intersecting line segments or "sides" that are joined pair-wise to form a closed path.
In mathematics, the sine is a trigonometric function of an angle.
In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel.
The small-angle approximation is a useful simplification of the basic trigonometric functions which is approximately true in the limit where the angle approaches zero.
In geometry, a solid angle (symbol) is a measure of the amount of the field of view from some particular point that a given object covers.
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
A spherical angle is a particular dihedral angle; it is the angle between two intersecting arcs of great circles on a sphere.
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.
A star is type of astronomical object consisting of a luminous spheroid of plasma held together by its own gravity.
In mathematics, a surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero.
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.
In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior.
A telescopic sight, commonly called a scope, is an optical sighting device that is based on a refracting telescope.
Thales of Miletus (Θαλῆς (ὁ Μιλήσιος), Thalēs; 624 – c. 546 BC) was a pre-Socratic Greek philosopher, mathematician, and astronomer from Miletus in Asia Minor (present-day Milet in Turkey).
Theta (uppercase Θ or ϴ, lowercase θ (which resembles digit 0 with horizontal line) or ϑ; θῆτα thē̂ta; Modern: θήτα| thī́ta) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth.
In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points.
A triangle is a polygon with three edges and three vertices.
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to it from known points.
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
A turn is a unit of plane angle measurement equal to 2pi radians, 360 degrees or 400 gradians.
Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere.
The 12-hour clock is a time convention in which the 24 hours of the day are divided into two periods: "The use of AM or PM to designate either noon or midnight can cause ambiguity.
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