Question : In $ΔABC, 2\angle A = 3\angle B = 6 \angle C$. What is the value of the largest angle among these three angles?
Option 1: $170^\circ$
Option 2: $90^\circ$
Option 3: $80^\circ$
Option 4: $150^\circ$
Correct Answer: $90^\circ$
Solution :
Given: $2\angle A = 3\angle B = 6 \angle C$
We know that,
$\angle A +\angle B + \angle C=180^\circ$
Putting the values, we get:
⇒ $\angle A +\frac{2}{3}\angle A + \frac{2}{6}\angle A=180^\circ$
⇒ $2\angle A =180^\circ$
⇒ $\angle A =90^\circ$
⇒ $\angle B=\frac{2}{3}×90^\circ=60^\circ, \angle C=\frac{1}{3}×90^\circ=30^\circ$
$\therefore\angle A $ is the largest angle = $90^\circ$
Hence, the correct answer is $90^\circ$.
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