Vertical Angle Theorem
The Vertical Angle Theorem is a theorem that states that all vertical angles are congruent.
Proof
Assume all angle measures to be in radians. A pair of vertical angles are formed by lines 
and 
and the intersection of these lines is P. Angles 
and 
are vertical angles. Let 
. From this, 
, so $m\angle BPD = \pi-(\pi-x)=x=m\angle APC.
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