MCQ
In Fig., if lines $l$ and $m$ are parallel lines, then $x =$
- A$70^{\circ}$
- ✓$40^{\circ}$
- C$100^{\circ}$
- D$30^{\circ}$
✓
Answer
Correct option: B.
$40^{\circ}$
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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