Question : In a $\triangle ABC$, if $2\angle A=3\angle B=6\angle C$, then the value of $\angle B$ is:
Option 1: $60^{\circ}$
Option 2: $30^{\circ}$
Option 3: $45^{\circ}$
Option 4: $90^{\circ}$
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Correct Answer: $60^{\circ}$
Solution :
Given: $2\angle A=3\angle B=6\angle C$
⇒ $ \angle A=3\angle C$
⇒ $\angle B=2\angle C$
In $\triangle ABC$,
$\angle A+\angle B+\angle C = 180^{\circ}$
⇒ $3\angle C+2\angle C+\angle C=180^{\circ}$
⇒ $6\angle C=180^{\circ}$
⇒ $\angle C=30^{\circ}$
$\therefore \angle B= 2 × 30^{\circ}= 60^{\circ}$
Hence, the correct answer is $60^{\circ}$.
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