In the given figure,find the values of x and | vedclass

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(C) $1$. From the figure,the angle $x$ and the angle $70^{\circ}$ are vertically opposite angles. Therefore,$x = 70^{\circ}$.$2$. The angle $y$ and th

Vedclass · Accepted Answer

$x=70^{\circ}, y=110^{\circ}$

Vedclass · Answer

(C) $1$. From the figure,the angle $x$ and the angle $70^{\circ}$ are vertically opposite angles. Therefore,$x = 70^{\circ}$.$2$. The angle $y$ and the angle $110^{\circ}$ form a linear pair on the line $PQ$. Therefore,$y + 110^{\circ} = 180^{\circ}$,which gives $y = 180^{\circ} - 110^{\circ} = 70^{\circ}$. Wait,looking at the figure,$y$ is vertically opposite to $110^{\circ}$,so $y = 110^{\circ}$.$3$. Alternatively,the interior angles on the same side of the transversal are $y$ and $x$. Since $y = 110^{\circ}$ and $x = 70^{\circ}$,their sum is $110^{\circ} + 70^{\circ} = 180^{\circ}$.$4$. Since the sum of the interior angles on the same side of the transversal is $180^{\circ}$,the lines $PQ$ and $XY$ must be parallel $(PQ \parallel XY)$.

In the given figure,find the values of $x$ and $y$ and then show that $PQ \parallel XY.$

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