In the figure, $l, m$ and $n$ are parallel lines intersected by transversal $p$ at $X, Y$ and $Z$ respectively. Find $\angle l, \angle 2$ and $\angle 3$."

Given:

$l, m$ and $n$ are parallel lines intersected by transversal $p$ at $X, Y$ and $Z$ respectively.

To do:

We have to find $\angle l, \angle 2$ and $\angle 3$.

Solution:

We know that,

Vertically opposite angles are equal.

Corresponding angles are equal.

Alternate angles are equal.

Therefore,

Let $\angle 4 = 120^o$

$\angle 2 = \angle 4$                   (Alternate angles)

$\angle 2 = 120^o$

$\angle 3 + \angle 4 = 180^o$                 (Linear pair)

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

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

$\angle 3 = 60^o$

$\angle 1 = \angle 3$                   (Corresponding angles)

$\angle 1 = 60^o$

Hence, $\angle 1 = 60^o, \angle 2 = 120^o, \angle 3 = 60^o$.

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Updated on: 10-Oct-2022

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