Question

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

Answer 1

In parallelogram $CLUE,$

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

$=\angle CEU$ [Opposite angles of a parallelogram are equal]

Now, in parallelogram $RISK,$ by using the property that the sum of adjacent angles of a parallelogram is equal to ${180}^{\circ },$

$\begin{array}{cc}\angle RKS+\angle KSI& ={180}^{\circ }\\ {120}^{\circ }+\angle KSI& ={180}^{\circ }\\ \angle KSI& ={180}^{\circ }-{120}^{\circ }\\ & ={60}^{\circ }\end{array}$

Now, we will apply the angle sum property in $△EOS,$

$\begin{array}{cc}\angle EOS+\angle SEO+\angle ESO& ={180}^{\circ }\\ x+{70}^{\circ }+{60}^{\circ }& ={180}^{\circ }\\ x+{130}^{\circ }& ={180}^{\circ }\\ x& ={50}^{\circ }\end{array}$