Geometry is one of the oldest branches of mathematics. It involves the study of the properties of points, lines, plane surfaces, and solid figures. Ancient Egyptian engineers used geometry when they built the pyramids, and modern trades workers use them when cutting sheet metal, installing plumbing, building cabinets, laying flooring and carpeting, and performing countless other tasks. The word "trigonometry" is derived from the Greek words meaning measurement of triangles. Trigonometry has application in navigation, surveying, construction, and many others branches of science, including mathematics and physics.

**Definition of angle**

An angle is a measure of the size of the opening between two intersecting lines. The point of intersection is called the vertex, and the lines forming the opening are called the sides or the arms of the angle.

**Classification**

The basic unit of measurement of angle size is the degree. Let`s review some basic terminology about angles. Recall the following dentitions from elementary geometry:

An angle is a right angle if it equals 90°

In trades geometry, angles are usually considered to be positive and not larger than 360°. (There is negative rake angle in cutting tool geometry and negative grade angle in a context of slopes.)

**Angles` relationships**

**Complementary Angles**

Two acute angles are complementary if their sum equals 90°. In other words, if 0°≤∠A, ∠B≤90° then ∠A and ∠B are complementary if ∠A+∠B = 90°.

**Supplementary Angles**

Two angles between 0° and 180° are supplementary if their sum equals 180°. In other words, if ∠A+∠B=180°.

**Conjugate or Opposite Angle**

Two angles between 0° and 360° are conjugate or opposite (or explementary) if their sum equals 360°. In other words, if ∠A+∠B=360°.