Question

Find x, y and z in the given parallelogram.

Answer 1

$ABCD$ is a given parallelogram, where $AB\parallel CD$ and $AD\parallel BC$

$\Rightarrow$ $\angle A+\angle B={180}^o$ [ In parallelogram sum of adjacent angles is supplementary ]

$\Rightarrow$ ${75}^o+x={180}^o$

$\Rightarrow$ $x={105}^o$

$\Rightarrow$ $\angle B=\angle D={105}^o$$ [ In parallelogram opposite angles are equal ]

$\Rightarrow$ $\angle A=\angle C={75}^o$ [ In parallelogram opposite angles are equal ]

$\therefore$ $y={75}^o$

$\Rightarrow$ $\angle ADC+\angle EDC={180}^o$ [ Linear pair ]

$\Rightarrow$ ${105}^o+z={180}^o$

$\Rightarrow$ $z={75}^o$