MCQ
In Fig. if lines $l$ and $m$ are parallel, then $x =$
- A$85^{\circ}$
- B$65^{\circ}$
- C$20^{\circ}$
- ✓$45^{\circ}$
✓
Answer
Correct option: D.
$45^{\circ}$
$l \| m$ 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)
$\angle2+\angle5+\angle3=180^\circ$
$20^{\circ} + 115^{\circ}+ x = 180^{\circ}$
$x = 45^{\circ}$.
$\angle2=20^\circ$
$\angle3=\text{x}$
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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