# Angles: What are Angles? Categories of Angles

### What are Angles?

Angles, triangles, squares, circles, cubes, cones and cylinders are all part of geometry in mathematics.

Geometry is the branch of mathematics that deals with the study of shapes, sizes and dimensions of a variety of things.

As a mathematics student, understanding angles is very important because it is vital in buildings, constructions and designs.

Sailors use angles to navigate their path along the sea while a carpenter can apply them to make beautiful designs of his job.

Amazingly, sport men and women can utilize angles in making an excellent performance. For instance, the use of angles can be applied when taking free throws in basket ball. Similarly, a footballer may utilize it to curl a free-kick into the football net.

By definition, an angle is a figure formed by two sides sharing a common endpoint.

As an instance to the above definition, an angle is formed where two walls in the corner of our homes meet or at the point where the two arms of a scissors meet.

The two sides that forms the angle are called arms or rays while the endpoint where both sides meet is called the vertex.

The figure below illustrates the arms and vertex of an angle:

The angle formed will depend on the amount of turn between each arm.

Below are some notable points from the above diagram:

• Most times, an angle is represented by the figure .
• The angle in the above figure can be represented as ABC.
• The unit of an angle is in degree. This implies that angles are measured in degrees and a protractor can be used to achieve this.

### Representation of Angles

Angles can be represented mainly in two ways. These are:

1. By using the three letters on the shape of the specific angle. Understand that the angle is formed on the middle letter, (vertex).

In tha above diagram, the angle will be represented as ABC

2. By giving the angle a name. The names are often denoted with a Greek letter like α (alpha) or θ (theta). Also, we can also name the angle with lowercase letters like 'p or q'.

Still using the above diagram as a basis, the angle will be labeled α

### Categories of Angles

An angle can be categorized as either interior or exterior based on where they are formed with regards to a shape. They are shown in the image below:

• Interior angles are formed inside a shape. In the above diagram, the angle is formed inside a triangle. (A triangle has 3 sides and 3 angles).

• Exterior angles are formed outside a shape via a line extending from the adjoining sides.