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Vertical Angles (also "opposite angles")
From Latin: verticalis "overhead"
Try this Drag an orange dot. Note the behavior of the vertical angles
∠JQM and ∠LQK.
As can be seen from the figure above, when two lines intersect,
four angles are formed. Each opposite pair are called vertical angles and are always
congruent.
The red angles ∠JQM and ∠LQK are equal,
as are the blue angles ∠JQL and ∠MQK.
Vertical angles are also called opposite angles.
Facts about vertical angles
They are congruent 
Vertical angles are always congruent, or of equal measure.
See ∠JQM and ∠LQK
in the figure above. Adjust the lines and convince yourself of this fact. 
Sum of vertical angles 
Both pairs of vertical angles (four angles altogether) always sum to a full angle (360°). 
Adjacent angles 
In the figure above, an angle from each pair of vertical angles are
adjacent angles and are
supplementary (add to 180°). For example, in the figure above, 

m∠JQL + m∠LQK = 180°. 

In the figure above, adjust the lines and convince yourself of this fact. 
About the word 'vertical'
'Vertical' has come to mean 'upright', or the opposite of horizontal. But here, it has more to do with the word 'vertex'.
Vertical angles are called that because they share a common vertex.
Related angle topics
General
Angle Types
Angle relationships
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