In the figures given below, decide whether l is parallel to m.

(i)

(ii)

(iii)

(iv)

(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

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