Do you mean "Are two vertical angles always congruent?" Vertical
angles are always congruent, but congruent angles do not have to be
vertical. Any two angles with the same angle measurement are
considered congruent by definition. The reason why vertical angles
are always congruent is explained below.
Imagine (or draw) an X forming 2 pairs of vertical angles. ∠1 is
to the left, ∠2 is on top, ∠3 is to the right, and ∠4 is on the
bottom. Vertical angles are always congruent because ∠1 and ∠2 are
supplementary, meaning that their measures add to 180 degrees. The
measures of ∠2 and ∠3 also add to 180 degrees. This means that
m∠1+m∠2=180 and m∠2+m∠3=180. Using the Transitive Property, it
becomes m∠1+m∠2=m∠2+m∠3. If you subtract the measure of ∠2 from
both sides, it becomes m∠1=m∠3. I hope that helped!