Question

In the given figure, p is a transversal to lines m and n, ∠2 = 120° and ∠5 = 60°. Prove that m || n.

Answer 1

The figure is given as follows:

It is given that p is a transversal to lines m and n .Also,

and .

We need to prove that

We have .

Also,and are vertically opposite angles, thus, these two must be equal. That is,

(i)

Also,.

Adding this equation to (i), we get :

But these are the consecutive interior angles.

Theorem states: If a transversal intersects two lines in such a way that a pair of consecutive interior angles is supplementary, then the two lines are parallel.

Thus, .

Hence, the lines are parallel to each other.