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.
|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.|
'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.