In the following figure RISK and CLUE are parallelograms.

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 :

$x+\angle \mathrm{ISK}+\angle \mathrm{CEU}=180^{\circ}$

$x=180^{\circ}-\left(70^{\circ}+60^{\circ}\right)$

$x=180^{\circ}-\left(70^{\circ}+60^{\circ}\right)=50^{\circ}$

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