angle

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An angle is the figure formed when two lines or rays meet at a point, and it measures how much one line is turned relative to the other. Angles are fundamental to geometry, mathematics, and practical fields like construction and navigation, where they help us describe and work with shapes, directions, and spatial relationships.

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Wikidata facts

Image: Coord Angle.svg

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Commons category: Angles (geometry)
Stack Exchange tag: stackoverflow.com/tags/angle
Unicode character: ∠

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~32 min read

Article

32 sections

Contents

Fundamentals
Notation and measurement
Units of measurement
Addition and subtraction
Common angles
Combining angle pairs
Polygon-related angles
Plane-related angles
Measuring angles <span class="anchor" id="Measurement"></span>
Reference angle
Circular measurement
Units
Dimensional analysis
Signed angles
Equivalent angles
Related quantities
Angles between curves
Bisecting and trisecting angles
Dot product and generalisations <span class="anchor" id="Dot product"></span>
Inner product
Angles between subspaces
Angles in Riemannian geometry
Hyperbolic angle
History and etymology
Vertical angle theorem
Angles in geography and astronomy
See also
Notes
References
Bibliography
Further reading
External links

In geometry, an angle is formed by two lines that meet at a point. Each line is called a side of the angle, and the point they share is called the vertex of the angle. The term angle is used to denote both geometric figures and their size or magnitude as associated quantity. Angular measure or measure of angle are sometimes used to distinguish between the measure of the quantity and figure itself. The measurement of angles is intrinsically linked with circles and rotation, and this is often visualized or defined using the arc of a circle centered at the vertex and lying between the sides.