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State whether the following is true or false.

In figure, lines l and m are parallel, but p and q are not.

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True

False

answer is A.

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Detailed Solution

Given, lines l and m are parallel, but p and q are not.
Question Image

If a transversal cuts two lines such that the sum of the interior angles on the same side of the transversal is

180 °

,then, the lines are parallel.
Adding the interior angles on the same side of the transversal in figure (a)

= 128 ° + 52 °

= 180 °

The sum of interior angles on the same side of the transversal is equal to

180 °

and so, the two lines are parallel.
Add interior angles on the same side of the transversal of the figure (b).

= 74 ° + 105 °

= 179 °

The sum of interior angles on the same side of the transversal is equal to

179 °

and so, the two lines are not parallel.
The lines l and m in the figure (a) are parallel but the lines p and q are not.
Therefore, option (1) is correct and the statement is true.

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