Question

Given that in $△ABC$, $\angle A={85}^{\circ }$ and $\angle B:\angle C=3:2$, then find $\angle B$ and $\angle C$

• A. ${57}^o$ and ${38}^o$
• B. ${38}^o$ and ${57}^o$
• C. ${60}^o$ and ${40}^o$
• D. ${90}^o$ and ${60}^o$

Answer 1

The correct option is A ${57}^o$ and ${38}^o$

Given, $\angle A={85}^{\circ }$
and $\angle B:\angle C=3:2$
Let $\angle B=3x$ and $\angle C=2x$
Sum of angles of a triangles $=180$
Therefore, $85+3x+2x=180$
$\Rightarrow 5x=95$
$\Rightarrow x=19$
Thus, $\angle B={57}^{\circ }$ and $\angle C={38}^{\circ }$