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# 9.In the above figure both RISK and CLUE are parallelograms. Find the value of x.

Here we have RISK and CLUE as two parallelograms.
$$∠1 = ∠L = 70^{\circ}\quad$$ [Opposite angles of a parallelogram]

$$∠K + ∠2 = 180^{\circ}$$

Sum of adjacent angles is $$180^{\circ}$$

$$120^{\circ} + ∠2 = 180^{\circ}$$

$$∠2 = 180^{\circ} – 120^{\circ} = 60^{\circ}$$

In ∆OES we have,

$$∠x + ∠1 + ∠2 = 180^{\circ}\quad$$ [Angle sum property]

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

$$\Rightarrow ∠x + 130^{\circ} = 180^{\circ}$$

$$\Rightarrow ∠x = 180^{\circ} – 130^{\circ} = 50^{\circ}$$

Hence $$∠x = 50^{\circ}$$