Q. 64.3( 72 Votes )

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Answer :

(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 = 75o


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 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.

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