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

#### Solution 1

Given:

`∠`4 = 110°, `∠`7 = 65°

To find: Is *m *|| *n*

Here, `∠`7 =`∠`5= 65° [Vertically opposite angle]

Now,

`∠`4 + `∠`5 = 110 + 65° = 175°

*∴m *is not parallel to n as the pair of co-interior angles is not supplementary.

#### Solution 2

The figure is given as follows:

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

∠4 = 110° and ∠7 = 65°.

We need check whether m||n or not.

We have.∠7 = 65°.

Also,∠7 5.and ∠5are vertically opposite angles, thus, these two must be equal. That is,

∠5 = °65.

Also, ∠4 =110°

Adding this equation to (i), we get:

∠4 + ∠5 =110° +65°

∠4 +∠5 =175°

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.