# Angle

something that is formed when two rays meet at a single or same point

When two straight lines come together, they make an angle. The two lines are called the sides[1] of the angle, and they meet at a point. A flat surface (called a plane) also forms an angle when it meets another.

To represent an angle, Greek letters such as ${\displaystyle \alpha }$ (alpha), ${\displaystyle \beta }$ (beta), ${\displaystyle \gamma }$ (gamma) and ${\displaystyle \theta }$ (theta) are sometimes used.[2] An angle indicates the space between its sides, or the amount of rotation needed to make one side coincide the other.[3][4]

To measure the size of an angle, we use units called degrees. A degree is a standard unit and we use the symbol ° after a number to show that it is a number of degrees. We can use a decimal number or a fraction for part of a degree, but a degree can also be divided into 60 minutes (1° = 60'), and a minute can be divided into 60 seconds (1' = 60"). So 22.5°, 2212° and 22° 30' are all the same angle.

In mathematics, angles can also be (and often are) measured in radians instead of degrees, by using the conversion factor ${\displaystyle 2\pi {\mbox{ rad}}=360^{\circ }}$ (for example, ${\displaystyle 22.5^{\circ }={\tfrac {\pi }{8}}{\mbox{ rad}}}$). Yet another unit of angle is gradian,[4] with ${\displaystyle 100{\text{ grad}}=90^{\circ }}$.

Angles are studied in geometry, where an angle where edges meet is often called a vertex. For example, the three sides of a triangle are its edges and two of the edges meet at each vertex. Similarly, two of the six sides (or faces) of a cube meet at each of its twelve edges, and three edges meet at each of its eight corners (or vertices, which is the plural version of vertex).

## Types of angles

### Individual angles

• In a zero angle the lines lie one upon the other thus creating a 0° angle aka the zero angle.
• An angle measuring greater (wider) than 0° but less (narrower) than 90° is called an acute angle.
• An angle more than 90° but less than 180° is called an obtuse angle.
• An angle that measures 180° is called a straight angle.
• An angle wider than 180° and narrower than 360° is called a reflex angle.
• An angle that has a made or full circle/completed 360° is called a full or complete angle.[5]

### Special angle pairs

In geometry, there are pairs angles having a special relationship with each other, making them interesting and convenient.

There is a pair of angles called complementary angles to which the sum of their measure (wideness) is equal to one right angle (which is equal to ${\displaystyle {\tfrac {1}{4}}}$  turn, 90°, or ${\displaystyle {\tfrac {\pi }{2}}}$  radians). Supplementary angles are also two angles, this time their combined measure is a straight angle (${\displaystyle {\tfrac {1}{2}}}$  turn, 180°, or ${\displaystyle \pi }$  radians). Two angles that total to a full angle (${\displaystyle 1}$  turn, 360°, or ${\displaystyle 2\pi }$  radians) are referred to as explementary or conjugate angles.

## References

1. Campana, D. M. (2016-09-06). The Teacher of Geometrical Drawing - For High Schools, Manual Training Schools, Technical Schools, Etc. Read Books Ltd. ISBN 978-1-4733-5366-4.
2. "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-08-17.
3. "Definition of angle | Dictionary.com". www.dictionary.com. Retrieved 2020-08-17.
4. Weisstein, Eric W. "Angle". mathworld.wolfram.com. Retrieved 2020-08-17.
5. "Angles - Acute, Obtuse, Straight and Right". www.mathsisfun.com. Retrieved 2020-08-17.