Question

In the figure, if $l_1||l_2$, what is the value of y?

Answer 1

In the figure, if $l_1||l_2$ and $l_3$ is the transversal

$x+y={180}^0$ ...(i)
(Linear pair)
$\angle 1=y$ ...(ii)
(Corresponding angles)
$\angle 1=3x$ ...(ii)
(Vertically opposite angles)
$\therefore y=3x$ (iv)
Now, $x+y={180}^0$
$\Rightarrow x+3x={180}^0$
$\Rightarrow 4x={180}^0$
$\therefore x=\frac{{180}^0}{4}={45}^0$
$\therefore y=3x=3\times {45}^0=135$