MCQ
In Figure. $PQ = PS.$ The value of $x$ is:
- A$35^\circ$
- ✓$45^\circ$
- C$55^\circ$
- D70°
✓
Answer
Correct option: B.
$45^\circ$
In $\triangle\text{PQS},$
$110^{\circ}+\angle\text{1}=180^{\circ}$ [linear pair of angles]
$\Rightarrow \ ∠\text{1}=180^{\circ}-110^{\circ}$
$\Rightarrow\angle\text{1}=70^{\circ}$
Also, $ \ ∠\text{1}=\angle\text{2}=70^{\circ}$ $[\because\text{PQ}=\text{PS}]$
As we know, the measures of any eterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles.
$\therefore \ \angle2=\text{x}+25^{\circ}$
$\Rightarrow 70^{\circ}=\text{x}+25^{\circ}$ $\because\angle2=70^{0}$
$\Rightarrow\text{x}=70^{\circ}-25^{\circ}$
$\Rightarrow \ \text{x}=45^{\circ}$
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