The angle symbol, followed by three points that define the angle, with the middle letter being the vertex, and the other two on the legs.
So in the figure above the angle would be ∠ABC or ∠CBA.
So long as the vertex is the middle letter, the order is not important. As a shorthand
we can use the 'angle' symbol. For example '∠ABC' would be read as 'the angle ABC'.

Or like this: ∠B

Just by the vertex, so long as it is not ambiguous. So in the figure above the angle could also be called simply
'∠B'

Measure of an angle

The size of an angle is measured in degrees (see Angle Measures). When we say 'the angle ABC' we mean the actual angle object.
If we want to talk about the size, or measure, of the angle in degrees, we should say 'the measure of the angle ABC' - often written m∠ABC.

However, many times we will see '∠ABC=34°'. Strictly speaking this is an error. It should say 'm∠ABC=34°'

Types of angle

Altogether, there are six types of angle as listed below. Click on an image for a full description of that type and a corresponding interactive applet.

When used in trigonometry,
angles have some extra properties:
They can have a measure greater than 360°, can be positive and negative, and are positioned on a coordinate grid with x and y axes.
They are usually measured in radians instead of
degrees.
For more on this see Angle definition and properties (trigonometry).

Angle construction

In the Constructions chapter, there are animated demonstrations of various
constructions
of angles using only a compass and straightedge.