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# Angle

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 [math]\alpha[/math] (alpha), [math]\beta[/math] (beta), [math]\gamma[/math] (gamma) and [math]\theta[/math] (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°, 22^{1}⁄_{2}° 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 [math]2\pi\mbox{ rad} = 360^\circ[/math] (for example, [math] 22.5^\circ = \tfrac{\pi}{8}\mbox{ rad}[/math]). Yet another unit of angle is gradian,^{[4]} with [math] 100 \text{ grad} = 90^{\circ}[/math].

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

•In a zero angle the lines lie one upon the other thus creating a 0° angle aka the zero angle.
•An angle greater than 0° but less than 90° is called an acute angle.
•An angle of 90° is called a right angle.
An angle greater than 90° but less than 180° is called an obtuse angle.
•An angle that measures 180° is called a straight angle.
An angle greater than 180° and less 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]}

Supplementary angles are two angles with the sum equal to 180°, and complementary angles are two angles with the sum equal to one right angle (90°). On the other hand, two angles that sum to one full circle (360°) are sometimes called explementary angles, or conjugate angles.

People usually use a protractor to measure and draw angles. Sometimes, people use a 360° protractor to measure angles.

## Related pages

## References

- ↑ Campana, D. M. (2016-09-06) (in en).
*The Teacher of Geometrical Drawing - For High Schools, Manual Training Schools, Technical Schools, Etc*. Read Books Ltd. . https://books.google.co.uk/books?id=5r_7DAAAQBAJ&pg=PA16&dq=called+%22sides+of+an+angle%22&hl=en&sa=X&ved=2ahUKEwi3lJG1p9LqAhXJTMAKHe1BAAoQ6AEwAnoECAkQAg#v=onepage&q=called%20%22sides%20of%20an%20angle%22&f=false. - ↑ "Compendium of Mathematical Symbols" (in en-US). 2020-03-01. https://mathvault.ca/hub/higher-math/math-symbols/.
- ↑ "Definition of angle | Dictionary.com" (in en). https://www.dictionary.com/browse/angle.
- ↑
^{4.0}^{4.1}Weisstein, Eric W.. "Angle" (in en). https://mathworld.wolfram.com/Angle.html. - ↑ "Angles - Acute, Obtuse, Straight and Right". https://www.mathsisfun.com/angles.html.