Question

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

• A. ${40}^{\circ }$
• B. ${46}^{\circ }$
• C. ${81}^{\circ }$
• D. ${85}^{\circ }$

Answer 1

The correct option is B ${46}^{\circ }$

Let measure of $\angle a=x$
$\therefore m\angle b=\frac{8}{9}x$ and $m\angle c=2x$

$\Rightarrow \angle a+\angle b+\angle c=180$

$\Rightarrow x+\frac{8}{9}x+2x=180$

$\Rightarrow \frac{9}{9}x+\frac{8}{9}x+\frac{18}{9}x=180$
$\Rightarrow \frac{9+8+18}{9}x=180$
$\Rightarrow \frac{35x}{9}=180$

$\Rightarrow x=\frac{180\times 9}{35}$

$\Rightarrow x={46}^{\circ }$