Angle

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

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[change | change source]

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]

The angles a and b are supplementary angles.

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.