Vertically opposite angles are always _______.

Vertically opposite angles are always equal. 

Explanation:

In the above figure,
$\angle 1 +\angle 2$  = 180° (Since they are a linear pair of angles) --------- (1)
$\angle 1 +\angle 4$ = 180° (Since they are a linear pair of angles) --------- (2)
From equations (1) and (2), 

$\angle 1 +\angle 2$ = 180° = $\angle 1 +\angle 4$.
According to the transitive property, if a = b and b = c then a = c. 

Therefore, we can rewrite the statement as $\angle 1 +\angle 2$ = $\angle 1 +\angle 4$ --------(3)
By eliminating $\angle 1$ on both sides of equation (3), we get $\angle 2 =\angle 4$
Similarly. we can use the same set of statements to prove that $\angle 1 =\angle 3$. 

Therefore, we conclude that vertically opposite angles are always equal