MCQ
In figure, if $l || m$, then $x =$
- ✓$105^\circ$
- B$65^\circ$
- C$40^\circ$
- D$25^\circ$
✓
Answer
Correct option: A.
$105^\circ$
From figure,
$\angle\text{AGE}=\angle\text{FGB}$ [Opposite angles]
$\Rightarrow\ \angle\text{FGB}=65^\circ$
Also,
$\angle\text{FGB}=\angle\text{HJI}$ [Corresponding angle]
$\Rightarrow\ \angle\text{HJI}=65^\circ$
Now, in $\angle\text{HJI},$
$\angle\text{HJI}+\angle\text{JIH}+\angle\text{IHJ}=180^\circ$
$\Rightarrow\ 65^\circ+40^\circ+\angle\text{IHJ}=180^\circ$
$\Rightarrow\ \angle\text{IHJ}=180^\circ-65^\circ-40^\circ=75^\circ$
Now,
$\text{x}=180^\circ-\angle\text{IHJ}=180^\circ-75^\circ$
$=105^\circ$
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