MCQ
In figure, $PQ \| RS$, $\angle\text{AEF}=95^\circ,\angle\text{BHS}=110^\circ$ and $\angle\text{ABC}=\text{x}^\circ.$ Then the value of $x$ is:
- A$15^\circ$
- ✓$25^\circ$
- C$70^\circ$
- D$35^\circ$
✓
Answer
Correct option: B.
$25^\circ$
From figure,
$\angle\text{AEF}=\angle\text{EGH}$ [Corresponding angles]
$\Rightarrow\ \angle\text{EGH}=\angle\text{AEF}=95^\circ$
Also,
$\angle\text{BGH}+\angle\text{EGH}=180^\circ$
$\Rightarrow\ \angle\text{BGH}=180^\circ-\angle\text{EGH}=180^\circ-95^\circ$
$=85^\circ$
$\angle\text{BHS}=110^\circ$
Now,
$\angle\text{BHG}+\angle\text{BHS}=180^\circ$
$\Rightarrow\ \angle\text{BHG}=180^\circ-\angle\text{BHS}=180^\circ-110^\circ$
$=70^\circ$
Now, in $\triangle\text{BHG}$
$\angle\text{BGH}+\angle\text{BGH}+\text{x}=180^\circ$ [Sum of all angles of a $\triangle$ is 180°]
$\Rightarrow\ 85^\circ+70^\circ+\text{x}^\circ=180^\circ$
$\Rightarrow\ \text{x}^\circ=180^\circ-155^\circ=25^\circ$
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