Question

Find the approximate value of $\angle A$ in $△ABC$ if $8\angle A=9\angle B=4\angle C$.

• A. ${70}^{\circ }$
• B. ${74}^{\circ }$
• C. ${81}^{\circ }$
• D. ${42.286}^{\circ }$

Answer 1

Answer: (D)

${42.286}^{\circ }$

Consider a triangle in which $\Delta ABC$ in which $8\angle A=9\angle B=4\angle C$.

Let, $\angle C=x$

Then,

$9\angle B=4x$

$\angle B=\frac{4x}{9}$

$8\angle A=4\angle C$

$8\angle A=4x$

$\angle A=\frac{1}{2}.x$

Now,

$\angle A+\angle B+\angle C={180}^0$

$\frac{1}{2}.x+\frac{4x}{9}+x={180}^0$

$\frac{9x+8x+18x}{18}={180}^0$

$\frac{35x}{18}={180}^0$

Hence,

$x=\frac{{180}^0\times 18}{35}$

$\angle A=\frac{1}{2}.x=\frac{{180}^0\times 18}{35\times 2}={42.28571}^0$

$\angle A={42.286}^0$

Hence, this is the answer.