The word "corner" has various interpretation. In geometry the corner is the part of the plane limited to two beams leaving one point – top. When it comes to the right, acute, developed angles, geometrical corners are meant.
As well as any figures in geometry, corners it is possible to compare. Equality of corners decides on the help of the movement. It is easy to divide a corner into two equal parts. It is a little more difficult to divide a figure into three parts, but nevertheless it can be done by means of a ruler and compasses. By the way, in the ancient time this task seemed quite difficult. To describe that one corner is more or less than another, geometrically simply.
As unit of measure of corners the degree – 1/180 part of the developed corner is accepted. The size of a corner is the number showing how much the corner chosen for unit of measure keeps within in the considered figure.
Each corner has a-degree measure, big zero. The developed corner is equal to 180 degrees. The-degree measure of a corner is considered to the equal sum of-degree measures of corners into which it breaks any beam on the plane limited to its parties. From any beam in the set plane it is possible to postpone a corner with some-degree measure which is not exceeding 180 degrees. And such corner will be only one. A measure of a flat corner which is a part of the half-plane the-degree measure of a corner with the similar parties is considered. A measure of the plane of the corner containing the half-plane is the value 360 – α where α – a-degree measure of an additional flat corner. The-degree measure of a corner gives the chance to pass from their geometric description to numerical. So, the corner equal to 90 degrees at right angle is understood, the obtuse angle is a corner, it is less than 180 degrees, but more than 90, the acute angle does not exceed 90 degrees. Besides-degree, there is a radian measure of the angle. In planimetry length of an arch of a circle is designated as L, radius – r, and the corresponding central corner – α. And these parameters are connected by a ratio α = L/r. This formula is the cornerstone of a radian measure of measurement of corners. If L=r, then a corner α is equal to one radian. So, the radian measure of the angle is the relation of length of the arch which is carried out by any radius and concluded between the parties of this corner to arch radius. A whole revolution in-degree measurement (360 degrees) corresponds 2π in radian. One radian is equal to 57.2958 degrees.