The complete flow proof is:
- [tex]\angle 5 = 40^o[/tex] ---- Given
- [tex]\angle 2 = 140^o[/tex] ---- Given
- [tex]\angle 5 + \angle 2 = 180^o[/tex] ----- [tex]\angle 5[/tex] and [tex]\angle 2[/tex] are supplementary angles
- [tex]\angle 5 + \angle 2 = 180^o[/tex] ----- [tex]\angle 5[/tex] and [tex]\angle 2[/tex] are same-side interior angles
- [tex]a ||b[/tex] ----- Proved
We have:
[tex]\angle 5 = 40^o[/tex]
[tex]\angle 2 = 140^o[/tex]
The proof of [tex]a ||b[/tex] is as follows:
The first statement is:
[tex]\angle 5 = 40^o[/tex] ---- Given
The next statement is:
[tex]\angle 2 = 140^o[/tex] ---- Given
Supplementary angles add up to [tex]180^o[/tex].
So, the third statement is:
[tex]\angle 5 + \angle 2 = 180^o[/tex] ----- [tex]\angle 5[/tex] and [tex]\angle 2[/tex] are supplementary angles
Same side of interior angles add up to [tex]180^o[/tex].
So, the fourth statement is:
[tex]\angle 5 + \angle 2 = 180^o[/tex] ----- [tex]\angle 5[/tex] and [tex]\angle 2[/tex] are same-side interior angles
Because the angles are supplementary angles and also same-side interior angles, then it means that line a is parallel to line b
So, the last statement is:
[tex]a ||b[/tex] ----- Proved
Read more about proofs of parallel lines at:
https://brainly.com/question/18396272
