Question

In the given figure, $l||m$. If $s$ and $t$ be transversals such that $s$ is not parallel to $t$. find the values of $x$ and $y$.

Answer 1

Lets form a figure, by arranging additional information in the figure.

It is given that, $l||m$

From the given figure:

$\angle 1=\angle 2={50}^{\circ }$ [$\because$ corresponding angles]

$\angle 1+\angle x={180}^{\circ }$ [$\because$ Linear pair]

$\Rightarrow \angle x={180}^{\circ }-\angle 1$

$\Rightarrow \angle x={180}^{\circ }-{50}^{\circ }$

$\Rightarrow \angle x={130}^{\circ }$ ---(1)

Now,

$\angle 2=\angle 4={65}^{\circ }$ [$\because$ corresponding angles]

$\angle 2+\angle y={180}^{\circ }$ [$\because$ Linear pair]

$\Rightarrow \angle y={180}^{\circ }-\angle 2$

$\Rightarrow \angle y={180}^{\circ }-{65}^{\circ }$

$\Rightarrow \angle y={115}^{\circ }$