Question

In the given figure, lines 𝑙 and 𝑚 are cut by a transversal line 𝑛. Check whether line 𝑙 is parallel to line 𝑚 or not.

Answer 1

Let us consider the two lines l, m and n is the transversal line intersecting l and m.

We know that the sum of interior angles on the same side of transversal is 180^o.
⇒ 123^o + ∠x
Here, ∠x = 57^o (vertically opposite angle)
⇒ 123^o + 57^o = 180^o

∴The sum of interior angles on the same side of transversal is equal to 180^o.
So, line l is parallel to line m.