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In the figure, $p$ is a transversal to lines $m$ and $n, \angle 2 = 120^o$ and $\angle 5 = 60^o$. Prove that $m \parallel n$."


Given:

$p$ is a transversal to lines $m$ and $n, \angle 2 = 120^o$ and $\angle 5 = 60^o$.

To do:

We have to prove that $m \parallel n$.

Solution:

From the figure,

$\angle 2 + \angle 3 = 180^o$                    (Linear pair)

$120^o+ \angle 3 = 180^o$

$\angle 3 = 180^o- 120^o$

$\angle 3= 60^o$

$\angle 3 = \angle 5$

Here, $\angle 3$ and $\angle 5$ are alternate angles

Therefore,

$m \parallel n$.

Hence proved.

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Updated on: 10-Oct-2022

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