A is the angle between plane of the two rays which have the same starting point or vertex. Usually measured in radian units such as the degree sexagesimal or Grad.

They can be defined on flat surfaces (plane trigonometry) or curved (spherical trigonometry). Dihedral angle is called the space between two half-planes whose common origin is a line. A solid angle is covered by an object seen from a given point, measuring its apparent size.

There are basically two ways to define an angle in the plane:

- Geometric: It's called "angle" to the width between any two lines meeting at a common point called the vertex. Colloquially, angle is the figure formed by two lines with a common origin. The angle between two curves is the angle between their tangent lines at the point of intersection.
- Trigonometric form: The amplitude of rotation or twist describes a rectilinear segment around one end as vertex taken from an initial position to a final position. If the rotation is counter-clockwise (counter-clockwise), the angle is considered positive. If the rotation is clockwise (according to clockwise), the angle is considered negative.

Euclid defines a mutual inclination angle as two lines that intersect with each other in a plane and are not straight. According to Proclus an angle must be a quality or quantity, or a relationship. The first concept was used by Eudemus of Rhodes, who described an angle as a deviation from a straight line, the second by Carpus of Antioch, who saw it as the interval or space between the intersecting lines; Euclid adopted the third concept, although their definitions of right angles, acute, and obtuse are quantitative.

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