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.

The magnitude of an angle is called an angular measure or simply "angle".

An angle must be defined as a quality, a quantity, or a relationship:

• Eudemus of Rhodes regarded an angle as a deviation from a straight line (quality).
• Carpus of Antioch regarded it as the interval or space between the intersecting lines (quantity).
• Euclid defined it as the inclination of two lines that meet each other and do not lie straight with respect to each other (relationship).

Angle comes from the Latin angulus, meaning 'corner'.

Notation

It is common to use lowercase Greek letters ($\alpha ,\beta ,\gamma ,\theta ,\phi ,\dots$) as variables to denote the size of some angle. Lowercase Roman letters ($a,b,c,\dots$) are also used.

We use three defining points to specify an angle; for example, the angle with vertex $A$ formed by the rays $\overrightarrow{AB}$ and $\overrightarrow{AC}$ may be specified $\mathrm{\angle }BAC$ $\angle BAC$. When it is reasonable to do so, angles may be denoted using the capital Roman letter denoting its vertex.