In Fig., if l | m, then x = - Vidyadip

MCQ

In Fig., if $l \| m,$ then $x =$

A
$40^{\circ}$
B
$25^{\circ}$
C
$65^{\circ}$
✓
$105^{\circ}$

✓

Answer

Correct option: D.

$105^{\circ}$

Given that,
$l \| m$ and n cuts them
Let,
$\angle1=65^\circ$
$\angle2=\text{x}$
$\angle3=40^\circ$
$\angle1+\angle4=65^\circ$ (Alternate angle) $(i)$
$\angle3+\angle4+\angle5=180^\circ$(Angle sum property)
$40^\circ+165^\circ+\angle5=180^\circ$
$\angle5=75^\circ$
Now,
$\angle2+\angle5=180^\circ$ (Linear pair)
$x + 75^{\circ}$ = 180$^{\circ}$
$x = 105^{\circ}$.

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