Definition: A shape, formed by two lines or rays diverging from a common point (the vertex).
Adjust the angle below by dragging the orange dot.
is the common point at which the two lines or rays are joined. Point B is the figure above is the vertex of the angle
||The legs (sides)
of an angle are the two lines that make it up. In the figure above, the line segments AB and BC
are the legs of the angle ∠ABC.
||The interior of an angle is the space in the 'jaws' of the angle extending out to infinity. See
Interior of an Angle
||All the space on the plane that is not the interior. See
Interior of an Angle
Identifying an angle
An angle can be identified in two ways.
Like this: ∠ABC
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
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
For more on this see Angle definition and properties (trigonometry).
In the Constructions chapter, there are animated demonstrations of various
of angles using only a compass and straightedge.
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Other angle topics
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