Question

If $PR\parallel TS$ and $PU\parallel RS$ then $x$ is equal to :

Answer 1

We have,

$PR||TS$ and $PU||RS$

Thus, We know that the sum of interior angles is ${180}^o$

$\angle RSU+\angle PUS={180}^o$

${40}^o+\angle PUS={180}^o$

$\angle PUS={140}^o$

So,

$\angle PUT={180}^o-{140}^o={40}^o$

Now in$△TPU$

$\angle PUS=\angle TPU+\angle TUP$

${140}^o=x+{40}^o$

$x={100}^o$