Yes, the lines are parallel.
What are parallel lines?
Parallel lines are coplanar straight lines that do not intersect at any point.
We have,
Line [tex]c[/tex] and [tex]d[/tex], and transversal [tex]e[/tex].
[tex]\angle 2 =\angle 3=\angle6=40^0[/tex],
And, [tex]\angle 1=140^0[/tex]
Now,
[tex]\angle 1=\angle4=140^0[/tex] (Vertically Opposite Angles)
So,
When a transversal line cuts two lines and sum of angles on the same side of the line is [tex]180^0[/tex] .
i.e. [tex]\angle6+\angle4=180^0[/tex]
[tex]140^0+40^0=180^0[/tex]
[tex]180^0=180^0[/tex]
So, sum of [tex]\angle6\ and\ \angle4[/tex] is [tex]180^0[/tex], that means line are parallel.
Hence, we can say that Yes, the lines are parallel.
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