MCQ
In a $\triangle \text{ABC},$ if $2\angle \text{A}=3\angle \text{B}=6\angle \text{C},$ then th s measure of the smallest angle is:
- A$90^\circ$
- B$60^\circ$
- C$40^\circ$
- ✓$30^\circ$
We have,
$2\angle \text{A}=3\angle \text{B}=6\angle \text{C}$
$\therefore 3\angle \text{B}=2\angle \text{A}$ and $6\angle \text{C}=2\angle \text{A}$
$\Rightarrow \angle \text{B}=\frac{2}{3}\angle \text{A}$ and $\angle \text{C}=\frac{2}{6}\angle \text{A}=\frac{1}{3}\angle \text{A}$
Now, $\angle \text{A}+\angle \text{B}+\angle \text{C}=180^\circ$ [Angle sum property of triangle$]$
$\Rightarrow \angle \text{A}+\frac{2}{3}\angle \text{A}+\frac{1}{3}\angle \text{A}=180^\circ$
$\Rightarrow 3\angle \text{A}+2\angle \text{A}+\angle \text{A}=180^\circ\times3$
$\Rightarrow 6\angle \text{A}=540^\circ$
$\Rightarrow \angle \text{A}=90^\circ$
$\therefore$ Smallest angle $=\angle \text{C}=\frac{1}{3}\angle \text{A}=\frac{1}{3}\times90^\circ$
$=30^\circ$
Hence, the correct answer is option $(d).$
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