Angle

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.

Fundamentals

There is no universally agreed definition of an angle. Angles can be conceived of and used in a variety of ways and while valid definitions may be given for specific contexts, it is difficult to give a single formal definition that is completely satisfactory in capturing all aspects of the general concept of angle.

One standard definition is that an angle is a figure consisting of two rays which lie in a plane and share a common endpoint. Alternatively, given such a figure, an angle might be defined as: the opening between the rays; the area of the plane that lies between the rays; or the amount of rotation about the vertex of one ray to the other.

More generally, angles are also formed wherever two line segments come together, such as at the corners of triangles and other polygons, or at the intersection of two planes or curves, in which case the rays lying tangent to each curve at the point of intersection define the angle.