Question
In Fig., if lines $l$ and $m$ are parallel lines, then $x =$
✓
Answer
Given that,
$l \ || \ m$
Let, $l \ || \ m$ and transversal cuts them and
$\angle1=70^\circ$
$\angle3=20^\circ$
$\angle4=30^\circ$
$\angle1+\angle2=180^\circ$ $($Interior angle$)$
$\angle2=110^\circ\text{(i})$
$\angle2=\angle5$ $($Vertically opposite angle$)$
$\angle5=110^\circ\text{(ii)}$
$\angle5+\angle3+\angle4=180^\circ$$($Sum of angles of a triangle is $180^\circ)$
$110^\circ + x + 30^\circ = 180^\circ$
$x = 40^\circ .$
$l \ || \ m$
Let, $l \ || \ m$ and transversal cuts them and
$\angle1=70^\circ$
$\angle3=20^\circ$
$\angle4=30^\circ$
$\angle1+\angle2=180^\circ$ $($Interior angle$)$
$\angle2=110^\circ\text{(i})$
$\angle2=\angle5$ $($Vertically opposite angle$)$
$\angle5=110^\circ\text{(ii)}$
$\angle5+\angle3+\angle4=180^\circ$$($Sum of angles of a triangle is $180^\circ)$
$110^\circ + x + 30^\circ = 180^\circ$
$x = 40^\circ .$
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