$In the given figure, ABCD is a parallelogram. From the given options, select the values of x and y.$

$[3 M a r k s]$

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Solution

We know that the opposite angles of a parallelogram are equal.

So,
$(3 x - 10)^{\circ} = (x + 80)^{\circ} \Rightarrow 3 x - x = 80^{\circ} + 10^{\circ} \Rightarrow 2 x = 90^{\circ} \Rightarrow x = 45^{\circ}$
$[1 M a r k]$

Also, the consecutive angles of a parallelogram are supplementary.

So,
$∠ B + ∠ C = 180^{\circ} (3 x - 10)^{\circ} + (y + 25)^{\circ} = 180^{\circ} (3 \times 45^{\circ}) - 10^{\circ} + y + 25^{\circ} = 180^{\circ} 135^{\circ} - 10^{\circ} + y + 25^{\circ} = 180^{\circ} \Rightarrow 125^{\circ} + y + 25^{\circ} = 180^{\circ} \Rightarrow y = 180^{\circ} - 125^{\circ} - 25^{\circ} \Rightarrow y = 30^{\circ}$
$[2 M a r k s]$

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