# 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 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 are often measured in radians instead of degrees ${\displaystyle (2\pi {\mbox{ rad}}=360^{\circ }}$, so ${\displaystyle 22.5^{\circ }={\tfrac {\pi }{8}}{\mbox{ rad}})}$.

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 of vertex).

## Types of angles

An acute angle is an angle less than 90° (but more than 0°). A right angle is an angle equal to 90°. An obtuse angle is an angle greater than 90° but less than 180°. A straight angle (or straight line) is an angle equal to 180°. A reflex angle is an angle greater than 180° but less than 360°.

Supplementary angles are two angles with the sum equal to 180°.

Two angles that sum to one right angle (90°) are called complementary angles.

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.

## 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.