How do you prove that vertical angles are congruent?

A pair of angles whose sides form two lines is called vertical angles. In the figure below, angles 1 and 3 are vertical angles since their sides form lines l and m. Similarly, angles 2 and 4 are vertical angles  for the same reason.

Vertical angles are congruent and it is easy to prove. We just use the fact that a linear pair of angles are supplementary; that is their measures add up to .  In the figure above, to prove that vertical angles are congruent,  we have to show that  and  are congruent or  and  are congruent.

Theorem

Vertical angles are congruent.

Proof

We show that .
 ** Linear pair of angles are supplementary. **Linear pair of angles are supplementary. ** Substitution property of equality; that is  .Substracting  from both sides, we have.Therefore, vertical angles are congruent. 

The answer would be $68.04