Question:
In the following figure RISK and CLUE are parallelograms. Find the measure of x.
Solution:
In the parallelogram RISK :
$\angle \mathrm{ISK}+\angle \mathrm{RKS}=180^{\circ}$ (sum of adjacent angles of a parallelogram is $180^{\circ}$ )
$\angle \mathrm{ISK}=180^{\circ}-120^{\circ}=60^{\circ}$
Similarly, in parallelogram CLUE :
$\angle \mathrm{CEU}=\angle \mathrm{CLU}=70^{\circ}$ (opposite angles of a parallelogram are equal)
In the triangle :
$x+\angle \mathrm{ISK}+\angle \mathrm{CEU}=180^{\circ}$
$x=180^{\circ}-\left(70^{\circ}+60^{\circ}\right)$
$x=180^{\circ}-\left(70^{\circ}+60^{\circ}\right)=50^{\circ}$