Question

In the following parallelograms, find the values of $x,y,z$(both figures)(in degrees)

Answer 1

For $fig.\left(i\right)$

As angles on one side of a line are always complementary.

$\therefore$ $x={90}^o$

$\Rightarrow$ $y={180}^o-({90}^o+30{)}^o$

$\therefore$ $y={60}^o$

The top vertex angle of the figure $\left(i\right)$ $={60}^o\times 2={120}^o$

$\Rightarrow$ Hence, bottom vertex $={120}^o$ [ Opposite angles of parallelogram are equal ]

$\therefore$ $z=\frac{1}{2}\times {120}^o={60}^o$

For $fig.\left(ii\right)$

$\Rightarrow$ $y={112}^o$ [ Opposite angles are equal in a parallelogram ]

$\Rightarrow$ $x={180}^o-({112}^o+{40}^o)$

$\therefore$ $x={28}^o$

$\Rightarrow$ $x=z$ [ Alternate angles between parallel lines ]

$\therefore$ $z={28}^o$