Question

In figure, $l,m$ and $n$ are parallel lines intersected by transversal $p$ at $X,Y$ and $Z$ respectively. Find $\angle 1,\angle 2$ and $\angle 3$

Answer 1

$\text{Given}:l,m\text{and}n\text{are parallel lines}$

$\angle Y={120}^{\circ }\left[\text{Vertically opposite angles}\right]$

$\text{Now},\angle 3+\angle Y={180}^{\circ }\left[\text{Linear pair}\right]$
$\Rightarrow \angle 3={180}^{\circ }-{120}^{\circ }$
$\Rightarrow \angle 3={60}^{\circ }$

$\text{Line}l\text{is parallel to line}m$,
$\therefore \angle 1=\angle 3\left[\text{Corresponding angles}\right]$
$\Rightarrow \angle 1={60}^{\circ }$

$\text{Also line}m\text{is parallel to line}n$,

$\angle 2={120}^{\circ }\left[\text{Alternate interior angles}\right]$

$\text{Hence},\angle 1={60}^{\circ },\angle 2={120}^{\circ }\text{and}\angle 3={60}^{\circ }$.