Question

In parallelogram PQRS, find $x,y,z$ and $w$.

Answer 1

$PQRS$ is a parallelogram

We know that, sum of adjacent angles of parallelogram is ${180}^o.$

$\therefore$ $\angle QPS+\angle PSR={180}^o$

$\Rightarrow$ $x+{110}^o={180}^o$

$\Rightarrow$ $x={70}^o$

We know that, opposite angles of a parallelogram are equal.

$\therefore$ $x=y={70}^o$ and $z={110}^o$

$\Rightarrow$ $\angle PSR+\angle PST={180}^o$ [ Linear pair ]

$\Rightarrow$ ${110}^o+w={180}^o$

$\Rightarrow$ $w={70}^o$

We get, $x={70}^o,y={70}^o,z={110}^o$ and $w={70}^o$