Question

In the above figure RISK and CLUE are parallelograms, Find the value of x.

Answer 1

Adjacent angles of a parallelogram are supplementary.

In parallelogram $RISK,\angle RKS+\angle ISK={180}^{\circ }$

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

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

Also, opposite angles of a parallelogram are equal.

In parallelogram $CLUE,\angle ULC=\angle CEU={70}^{\circ }$

The sum of the measures of all the interior angles of a triangle is ${180}^{\circ }$.

$x+{60}^{\circ }+{70}^{\circ }={180}^{\circ }$
$x+{130}^{\circ }={180}^{\circ }$
$x={180}^{\circ }-{130}^{\circ }$

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