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Vertical Angles (also "opposite angles")
From Latin: verticalis "overhead"
Definition: A pair of non-adjacent angles formed by the intersection of two straight lines
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,
  mJQL + mLQK = 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.

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Other angle topics

General

Angle Types

Angle relationships