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°, 221⁄2° 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[change]
Individual angles[change]
- 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 90° wide is called a right 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[change]
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 <math>\tfrac{1}{4}</math> turn, 90°, or <math>\tfrac{\pi}{2}</math> radians). Supplementary angles are also two angles, this time their combined measure is a straight angle (<math>\tfrac{1}{2}</math> turn, 180°, or <math>\pi</math> radians). Two angles that total to a full angle (<math>1</math> turn, 360°, or <math>2\pi</math> radians) are referred to as explementary or conjugate angles.
Related pages[change]
References[change]
- ↑ 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.
- ↑ "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-08-17.
- ↑ "Definition of angle | Dictionary.com". www.dictionary.com. Retrieved 2020-08-17.
- ↑ 4.0 4.1 Weisstein, Eric W. "Angle". mathworld.wolfram.com. Retrieved 2020-08-17.
- ↑ "Angles - Acute, Obtuse, Straight and Right". www.mathsisfun.com. Retrieved 2020-08-17.
