Angles 2 and 3 are supplementary, therefore their measures add to 180°:   

m∠2 + m∠3 = 180°      

m∠2 = 180°  -  m∠3    (1)



Angles 4 and 3 are also supplementary, therefore their measures add to 180°:

m∠4 + m∠3 = 180° 

m∠4 = 180° -  m∠3     (2)



Compare (1) to (2).  Do you see it?   



If  a = c  and b = c  then a = b.   



I left the measure of angle 2 out of the proof because it doesn't matter what its measure is,  angle 2 and angle 4 will ALWAYS be equal (vertical angles are always equal).  



  

 

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