Question

In the given figure, transversal l intersects two lines m and n, ∠4 = 110° and ∠7 = 65°. Is m || n ?

Answer 1

The figure is given as follows:

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

and .

We need check whether or not.

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 which are not supplementary.

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, m is not parallel to n.