##### 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 126o and 44o 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 = 126o + 44o

= 170o

Hence,

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

Therefore,

The lines l and m are not parallel to each other

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

Therefore,

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

x = 180o – 75o

= 105o

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 = 105o

And,

ABC = 105o

Therefore,

Lines l and m are not parallel to each other

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

Therefore,

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

x = 180o – 123o

= 57o

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

For this,

Corresponding angles ABC and x should be equal

x = 57o

And,

ABC = 57o

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 98o are forming a linear pair on the line l

Therefore,

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

x = 180o – 98o

= 82o

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 = 82o

And,

ABC = 72o

Therefore,

Lines l and m are not parallel to each other

11