Question

In the following figure, find the value of x for which the lines l and m are parallel.

Answer 1

Let us draw the figure as below -

It is given to us that l and m are parallel to each other.

Here, n is a transversal intersecting l and m which are parallel to each other.

Also, we have ∠pqm = 44°  ...(i)

We have to find the value of x, i.e., ∠qpl

We know, if a transversal intersects two parallel lines then each pair of corresponding angles is equal.

Here, the transversal n intersects two parallel lines l and m. So, the following holds true for the corresponding angles.

∠pqm = ∠npl

⇒ ∠npl = 44° (From (i), we have ∠pqm = 44°)  ...(ii)

Again, the linear pair axiom states that

If a ray stands on a line, then the sum of two adjacent angles so formed is 180°.

Here, we can see that l is a ray standing on the line n.

⇒ ∠npl + ∠lpq = 180°  ...(By linear pair axiom)

⇒ 44° + ∠lpq = 180°

⇒ ∠lpq = 180° – 44°

⇒ ∠lpq = 136°

⇒ x = 136°

Thus, the value of x is equal to 136°.