(i) From the above figure,

There are two angles 126^o and 44^o which are on the same side of the transversal line n

Let us consider two lines l and m

Also,

There is a transversal line n which is intersecting both the lines

Therefore,

Sum of interior angles on the same side of the transversal = 126^o + 44^o

= 170^o

Hence,

It is clear that the sum of interior angles which are on the same side of the transversal is not equal to 180^o

Therefore,

The lines l and m are not parallel to each other

(ii) In the above question we have, Angle x and 75^o are forming a linear pair on the line l

Therefore,

x + 75^o = 180^o (Sum of angles of linear pair)

x = 180^o – 75^o

= 105^o

We have to show that l and m are parallel to each other

For this,

Corresponding angles ∠ABC and ∠x should be equal

But,

∠x = 105^o

And,

∠ABC = 105^o

Therefore,

Lines l and m are not parallel to each other

(iii) In the above question we have, Angle x and 123^o are forming a linear pair on the line m

Therefore,

x + 123^o = 180^o (Sum of angles of linear pair)

x = 180^o – 123^o

= 57^o

We have to show that l and m are parallel to each other

For this,

Corresponding angles ∠ABC and ∠x should be equal

∠x = 57^o

And,

∠ABC = 57^o

Therefore,

Both the angles are equal to each other

Hence,

Lines l and m are not parallel to each other

(iv) In the above question we have, Angle x and 98^o are forming a linear pair on the line l

Therefore,

x + 98^o = 180^o (Sum of angles of linear pair)

x = 180^o – 98^o

= 82^o

We have to show that l and m are parallel to each other

For this,

Corresponding angles ∠ABC and ∠x should be equal

But,

∠x = 82^o

And,

∠ABC = 72^o

Therefore,

Lines l and m are not parallel to each other