If angle one and angle two form a linear pair, and angle two and angle three are supplementary, prove angle one and angle three are congruent

Question

lines are two in a somewhat horizontal parrallel that intersect a vertical

angle one is acute and angle two is obtuse

Answer 1

angle one and angle two form a linear pair

 

< 1  + < 2 = 180

 

<1 = 180 - <2  ---------- eq 1

angle two and angle three are supplementary

 

< 2 +< 3 = 180

 

<3 = 180 - <2 -----------eq 2

 

so from eq 1 and eq 2

 

<1 and <3 are congurent