Question

In the following parallelogram $ABCD$, find the values of $x$ and $y$. Mention the property used.

Answer 1

$ABCD$ is a parallelogram, with diagonals $AC$ and $BD$ intersect at point $O$.

$\Rightarrow$ $\angle A+\angle B={180}^o$ [ Sum of adjacent angles are supplementary in parallel ]

$\Rightarrow$ ${110}^o+({40}^o+x)={180}^o$

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

$\Rightarrow$ $x={30}^o$

In $△OBC,$

$\Rightarrow$ $\angle OBC+\angle BCO+\angle COB={180}^o$

$\Rightarrow$ $x+{50}^o+y={180}^o$

$\Rightarrow$ ${30}^o+{50}^o+y={180}^o$

$\Rightarrow$ ${80}^o+y={180}^o$

$\therefore$ $y={100}^o$

$\therefore$ $x={30}^o,y={100}^o$