# The Definition of an Angle

## Types of Angles in Math Terms

In mathematics, particularly geometry, angles are formed by two rays (or lines) that begin at the same point or share the same endpoint. The angle measures the amount of turn between the two arms or sides of an angle and is usually measured in degrees or radians. Where the two rays intersect or meet is called the vertex.

An angle is defined by its measure (for example, degrees) and is not dependent upon the lengths of the sides of the angle.

### History of the Word

The word "angle" comes from the Latin word angulus, meaning "corner." It is related to the Greek word ankylοs meaning "crooked, curved," and the English word "ankle." Both Greek and English words come from the Proto-Indo-European root word "ank-" meaning "to bend" or "bow."

### Types of Angles

Angles that are exactly 90 degrees are called right angles. Angles less than 90 degrees are called acute angles. An angle that is exactly 180 degrees is called a straight angle (this appears as a straight line). Angles that are greater than 90 degrees and less than 180 degrees are called obtuse angles. Angles that are larger than a straight angle but less than 1 turn (between 180 degrees and 360 degrees) are called reflex angles. An angle that is 360 degrees, or equal to one full turn, is called a full angle or complete angle.

For an example of an obtuse angle, the angle of a typical house rooftop is often formed at an obtuse angle.

An obtuse angle is greater than 90 degrees since water would pool on the roof (if it was 90 degrees) or if the roof did not have a downward angle for water to flow.

### Naming an Angle

Angles are usually named using alphabet letters to identify the different parts of the angle: the vertex and each of the rays.

For example, angle BAC, identifies an angle with "A" as the vertex. It is enclosed by the rays, "B" and "C." Sometimes, to simplify the naming of the angle, it is simply called "angle A."