MCQ
In figure, what is the value of $x?$
- A$35$
- B$50$
- C$45$
- ✓$60$
✓
Answer
Correct option: D.
$60$
In $\triangle\text{ABC},$
$\angle\text{BCA} + \angle\text{CAB} + \angle\text{ABC} = 180^\circ$
$\Rightarrow 3\text{y}^\circ+\text{x}^\circ+5\text{y}^\circ = 180^\circ$
$\Rightarrow 8\text{y}^\circ+\text{x}^\circ = 180^\circ \ ...\ (\text{i})$
Also, $5\text{y}^\circ = 180^\circ - 7\text{y}^\circ$
$\Rightarrow 12\text{y}^\circ=180^\circ$
$\Rightarrow \text{y}^\circ=15^\circ$
From (i), $\text{x}^\circ=180^\circ−8\text{y}^\circ$
$\Rightarrow \text{x}^\circ=180^\circ−8\times 15^\circ$
$\Rightarrow \text{x}^\circ=60^\circ$
$\angle\text{BCA} + \angle\text{CAB} + \angle\text{ABC} = 180^\circ$
$\Rightarrow 3\text{y}^\circ+\text{x}^\circ+5\text{y}^\circ = 180^\circ$
$\Rightarrow 8\text{y}^\circ+\text{x}^\circ = 180^\circ \ ...\ (\text{i})$
Also, $5\text{y}^\circ = 180^\circ - 7\text{y}^\circ$
$\Rightarrow 12\text{y}^\circ=180^\circ$
$\Rightarrow \text{y}^\circ=15^\circ$
From (i), $\text{x}^\circ=180^\circ−8\text{y}^\circ$
$\Rightarrow \text{x}^\circ=180^\circ−8\times 15^\circ$
$\Rightarrow \text{x}^\circ=60^\circ$
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