Question

In the following figure, $ABCD$ and $PORS$ are two parallelograms such that $\angle D={120}^o$ and $\angle Q={70}^o$. Find the value of $x$

Answer 1

Since $PQRS$ is parallelogram

$\angle S=\angle Q$ (opposite angles of a parallelogram)

$\angle S={70}^{\circ }$

Now, $ABCD$ is a parallelogram

$\angle D+\angle C={180}^{\circ }$

${120}^{\circ }+\angle C={180}^{\circ }$

$\angle C={60}^{\circ }$

Therefore, $\angle S+\angle C+x={180}^{\circ }$

${70}^{\circ }+{60}^{\circ }+x={180}^{\circ }$

$x={50}^{\circ }$