In a , if 3 =4 =6 , calculate the angles.

Question

In a $\triangle\text{ABC},$ if $3\angle\text{A}=4\angle\text{B}=6\angle\text{C},$ calculate the angles.

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Answer

In a $\triangle\text{ABC}$
$3\angle\text{A}=4\angle\text{B}=6\angle\text{C}=1$ (say)
$\therefore\angle\text{A}=\frac{1}{3}$
$\angle\text{B}=\frac{1}{4}$
$\angle\text{C}=\frac{1}{6}$
$\therefore$ Ratio $=\frac{1}{3}:\frac{1}{4}:\frac{1}{6}=\frac{4:3:2}{12}$
$(LCM of 3, 4, 6 = 12)$
Sum of angles $\triangle\text{ABC}=180^\circ$
$\therefore\angle\text{A}=\frac{180^\circ\times4}{4+3+2}=\frac{180^\circ\times4}{9}=80^\circ$
$\angle\text{B}=\frac{180^\circ\times3}{9}=60^\circ$
$\angle\text{C}=\frac{180^\circ\times2}{9}=40^\circ$
Hence, angles of $\triangle\text{ABC}$ are$ 40^\circ , 60^\circ $and $40^\circ .$

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