Mark ( ) against the correct answer: In a , If 2 =3 =6 then =? - Vidyadip

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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