Question
In Fig. if lines $l$ and $m$ are parallel, then $x =$
✓
Answer
$l \ || \ m$
Let transversal be n and $\angle1=65^\circ$
$\angle2=20^\circ$
$\angle3=\text{x}$
Since,
$l \ || \ m$ and $n$ cuts them so,
$\angle1+\angle4=180^\circ$ $($Co. interior angle$)$
$65^\circ+\angle4=80^\circ$
$\angle4=115^\circ\text{(i)}$
$\angle4=\angle5=115^\circ$ $($Vertically opposite angle$)$
$\angle2+\angle5+\angle3=180^\circ$
$20^\circ + 115^\circ + x = 180^\circ$
$x = 45^\circ .$
Let transversal be n and $\angle1=65^\circ$
$\angle2=20^\circ$
$\angle3=\text{x}$
Since,
$l \ || \ m$ and $n$ cuts them so,
$\angle1+\angle4=180^\circ$ $($Co. interior angle$)$
$65^\circ+\angle4=80^\circ$
$\angle4=115^\circ\text{(i)}$
$\angle4=\angle5=115^\circ$ $($Vertically opposite angle$)$
$\angle2+\angle5+\angle3=180^\circ$
$20^\circ + 115^\circ + x = 180^\circ$
$x = 45^\circ .$
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