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 $\frac{2}{3}xand\frac{3}{2}x$
$\Rightarrow \frac{2}{3}x+\frac{3}{2}x+{50}^{\circ }={180}^{\circ }$
$\Rightarrow \frac{4x+9x}{6}={130}^{\circ }$
$\Rightarrow 13x={130}^{\circ }\times 6$
$\Rightarrow x=\frac{{780}^{\circ }}{13}={60}^{\circ }$.
$Now,\frac{2}{3}\times 60={40}^{\circ }and\frac{3}{2}\times 60={90}^{\circ }$.
Hence, the required angles are ${40}^{\circ },{90}^{\circ }$.