Answer:
Because Alternate Interior angles are equal.
Step-by-step explanation:
STEP - I:
[tex]$ m \angle {5} = 3 . m \angle {\{3}\} $[/tex]
Reason:
This is the given data.
STEP - II:
It has multiplied and the reason is mentioned as well.
STEP - III:
[tex]$ m \angle{3} + m \angle{5} $[/tex] = 45° + 135° = 180°
Reason:
It has substituted the value of [tex]$ m\angle{5} $[/tex] from the previous step. The sum of [tex]$ m\angle{3} $[/tex] and [tex]$ m \angle{5} $[/tex] is 180°.
STEP - IV:
[tex]$ a \parallel b $[/tex]
Reason:
We calculated [tex]$ m\angle{5}[/tex] to be 135°.
Note that [tex]$ \angle {5} $[/tex] and [tex]$ \angle{6} $[/tex] are on the same line. That means their sum should be 180°.
i.e., [tex]$ m\angle{5} + m\angle{6} $[/tex] = 180°.
[tex]$ \implies $[/tex] 135° + [tex]$ m\angle{6} $[/tex] = 180°.
[tex]$ \implies m\angle{6} = $[/tex] 45°.
One of the ways to prove [tex]$ a \parallel b $[/tex] is to check if alternate interior angles are equal.
Here, [tex]$ m\angle{3} $[/tex] and [tex]$ m \angle {6} $[/tex] are alternate interior angles and they are equal.
[tex]$ \implies a \parallel b $[/tex].
