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Question : In a triangle ABC; 8$\angle$A = 6$\angle$B = 3$\angle$C. What are the degree measures of $\angle$ A, $\angle$ B, and $\angle$C?

Option 1: $48^{\circ}, 96^{\circ}, \text{and } 36^{\circ}$

Option 2: $36^{\circ}, 96^{\circ}, \text{and } 48^{\circ}$

Option 3: $36^{\circ}, 48^{\circ}, \text{and } 96^{\circ}$

Option 4: $96^{\circ}, 48^{\circ}, \text{and } 36^{\circ}$


Team Careers360 2nd Jan, 2024
Answer (1)
Team Careers360 6th Jan, 2024

Correct Answer: $36^{\circ}, 48^{\circ}, \text{and } 96^{\circ}$


Solution : Given: 8$\angle$A = 6$\angle$B
$⇒\angle$A = $\frac{6}{8}\angle$B = $\frac{3}{4}\angle$B ----------------(i)
Also, 6$\angle$B = 3$\angle$C
$⇒\angle$C = $\frac{6}{3}\angle$B = 2$\angle$B ---------------(ii)
Now, $\angle$A + $\angle$B + $\angle$C = $180^{\circ}$
$⇒\frac{3}{4}\angle$B + $\angle$B + 2$\angle$B = $180^{\circ}$
$⇒\frac{15}{4}\angle$B = $180^{\circ}$
$⇒\angle$B = $48^{\circ}$
So, $\angle$A = $\frac{3}{4}×48^{\circ}=36^{\circ}$
$⇒\angle$C = 2 × $48^{\circ}=96^{\circ}$
Hence, the correct answer is $36^{\circ}, 48^{\circ}, \text{and } 96^{\circ}$.

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