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Which pair of lines in the figure are parallel? Give reasons."


To do:

We have to find which of the given pairs of lines are parallel.

Solution:

In the given figure,

$\angle A = 115^o, \angle B = 65^o, \angle C = 115^o$ and $\angle D = 65^o$

$\angle A + \angle B = 115^o+ 65^o$

$ = 180^o$

Here, $\angle A$ and $\angle B$ are co-interior angles.

Therefore,

$AD \parallel BC$

Similarly,

$\angle A + \angle D = 115^o + 65^o$

$ = 180^o$

Here, $\angle A$ and $\angle D$ are co-interior angles.

Therefore,

$AB \parallel DC$.

Hence, $AD \parallel BC$ and $AB \parallel DC$.

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Updated on: 10-Oct-2022

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