Question

Two angles of a triangle are in the ratio $\frac{2}{3}:\frac{3}{2}$ and the third angle is ${50}^{\circ }$. The two angles are:

• A. ${30}^{\circ },{95}^{\circ }$
• B. ${45}^{\circ },{85}^{\circ }$
• C. ${30}^{\circ },{100}^{\circ }$
• D. ${40}^{\circ },{90}^{\circ }$

Answer 1

The correct option is D ${40}^{\circ },{90}^{\circ }$

Let the two angles of the triangle be $\left(\frac{2x}{3}\right)$ and $\left(\frac{3x}{2}\right)$
$\Rightarrow \left(\frac{2x}{3}\right)+\left(\frac{3x}{2}\right)+{50}^{\circ }={180}^{\circ }$
$\Rightarrow \frac{(4x+9x)}{6}={130}^{\circ }$
$\Rightarrow 13x={130}^{\circ }\times 6$
$\Rightarrow x=\frac{{780}^{\circ }}{13}={60}^{\circ }$

Now $\frac{2}{3}\times 60={40}^{\circ }$ and $\frac{3}{2}\times 60={90}^{\circ }$
Hence the required angles are ${40}^{\circ }$ and ${90}^{\circ }$