MCQ
Mark $(\checkmark)$ against the correct answer: In a $\triangle\text{ABC},$ If $2\angle\text{A}=3\angle\text{B}=6\angle\text{C}$ then $\angle\text{B}=?$
- A$30^\circ $
- B$45^\circ $
- ✓$60^\circ $
- D$90^\circ $
✓
Answer
Correct option: C.
$60^\circ $
Given:
$2\angle\text{A}=3\angle\text{B}$
$\angle\text{A}=\frac{3}{2}\angle\text{B}\ \dots(\text{i})$
$3\angle\text{B}=6\angle\text{C}$
$=\angle\text{C}=\frac{1}{2}\angle\text{B}\ \dots(\text{ii})$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$\Rightarrow\frac{3}{2}\angle\text{B}+\angle\text{B}+\frac{1}{2}\angle\text{B}=180^\circ$
$\Rightarrow(\frac{3}{2}+1+\frac{1}{2})\angle\text{B}=180^\circ$
$\Rightarrow\frac{6}{2}\angle\text{B}=180^\circ$
$\Rightarrow\angle\text{B}=\frac{180^\circ}{3}=60^\circ$
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