Question

$EFGH$ is a parallelogram. Find the values of $x,y$ and $z$.

Answer 1

$\because EFGH$ is a parallelogram.

$\Rightarrow$ $\angle FGH+\angle FGK={180}^o$ [ Linear pair ]

$\Rightarrow$ $\angle FGH+{70}^o={180}^0$

$\therefore$ $\angle FGH={110}^o$

$\Rightarrow$ $\angle FGH=\angle FEH={110}^o$ [ Opposite angles of a parallelogram are equal ]

$\therefore$ $x={110}^o$

Now, $\angle EHG+\angle FGH={180}^o$ [ Sum of adjacent angles of parallelogram is ${180}^o.$ ]

$\Rightarrow$ $\angle EHF+\angle FHG+\angle FGH={180}^o$

$\Rightarrow$ ${40}^o+z+{110}^o={180}^o$

$\Rightarrow$ $z+{150}^o={180}^o$

$\therefore$ $z={30}^o$

$\Rightarrow$ $\angle EHG={40}^o+z$

$={40}^o+{30}^o$

$\Rightarrow \angle EHG={70}^o$

$\Rightarrow$ $\angle FHG+\angle HGF+\angle GFH={180}^o$ [ Sum of angles of triangle is ${180}^o$ ]

$\Rightarrow$ ${30}^o+{110}^o+y={180}^o$

$\Rightarrow$ ${140}^o+y={180}^o$

$\therefore$ $y={40}^o$

We get, $x={110}^o,y={40}^o,z={30}^o$