angle 1 is vertical to angle 2. therefore, angle 1 is congruent to angle 2 why is this true?

Question

idk the answer

 

Answer 1

 

Proof:

 

 

    In order for  Angle 1 and Angle 2 to be vertical angles, they must both

    be supplementary to the same angle.

 

    For construction, two intersecting lines L and M, with line L running east to west and

   line M running north to south. Angle 1 is the Northeast corner while

    Angle 2 is the southeast corner of the intersection, making them vertical angles.

In the northwest corner in angle 3.

 

   Since they are on the same line L, angles 1 and 3 are supplementary, so angle 1 + angle 3 = 180.

   Since they are on the same line M, angles 2 and 3 are supplementary, so angle 2 + angle 3 = 180.

 

  Setting these equations equal to each other, as they both equal 180, by transitive /substitution, it is :

          angle 1 + angle 3 = angle 2 + angle 3

 

   Subtracts angle 3 from both sides,  angle 1 = angle 2

 

 [end of proof]