Noun

Singular angle

Plural angles

angle (plural angles)

1. (geometry) A figure formed by two rays which start from a common point (a plane angle) or by three planes that intersect (a solid angle).

   the angle between lines A and B

2. (geometry) The measure of such a figure. In the case of a plane angle, this is the ratio (or proportional to the ratio) of the arc length to the radius of a section of a circle cut by the two rays, centered at their common point. In the case of a solid angle, this is the ratio of the surface area to the square of the radius of the section of a sphere.

   The angle between lines A and B is π/4 radians, or 45 degrees.

3. A corner where two walls intersect.

   an angle of a building

4. A change in direction.

   The horse took off at an angle.

5. A viewpoint.

   Look at it from this angle.

6. (media) The focus of a news story, either in print or broadcasting.
7. (slang, professional wrestling) A storyline between two wrestlers, providing the background for and approach to a feud.
8. (slang) A scheme; a means of benefitting from a situation, usually hidden, possibly illegal.

   His angle is that he gets a percentage, but mostly in trade.

Synonyms

• (corner): corner
• (change in direction): swerve, tangent
• (vertex): -gon (as per hexagon)
• (viewpoint): opinion, perspective, point of view, slant, view, viewpoint

Derived terms

• acute angle
• acute-angled
• angle quote
• angle bracket
• central angle
• complementary angle
• dihedral angle

• exterior angle
• interior angle
• oblique angle
• obtuse angle
• obtuse-angled
• opposite angle

• pentangle
• plane angle
• quadrangle
• rectangle
• reflex angle
• right angle

• round angle
• solid angle
• straight angle
• supplementary angle
• triangle
• vertical angle

Related terms

• angular
• angulate
• angulation

In geometry and trigonometry, an angle (in full, plane angle) is the figure formed by two rays sharing a common endpoint, called the vertex of the angle (Sidorov 2001). The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other (see "Measuring angles", below). Where there is no possibility of confusion, the term "angle" is used interchangeably for both the geometric configuration itself and for its angular magnitude (which is simply a numerical quantity).

The word angle comes from the Latin word angulus, meaning "a corner". The word angulus is a diminutive, of which the primitive form, angus, does not occur in Latin. Cognate words are the Latin angere, meaning "to compress into a bend" or "to strangle", the Greek ἀγκύλος (ankylοs), meaning "crooked, curved," and the English word "ankle." All three are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow" (Slocum 2007).

Euclid 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. According to Proclus an angle must be either a quality or a quantity, or a relationship. 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, although his definitions of right, acute, and obtuse angles are certainly quantitative.