Question

In a triangle, the angles are in ratio $1:3:2$. Find the difference between the greatest and smallest angle of the triangle.

• A. ${10}^o$
• B. ${70}^o$
• C. ${60}^o$
• D. ${20}^o$

Answer 1

The correct option is C ${60}^o$

Given, the angles are in the ratio $1:3:2$.

Let the angles be $x,3x$ and $2x$.

Using angle sum property of triangle,

$x+3x+2x={180}^{\circ }\Rightarrow 6x={180}^{\circ }\Rightarrow x={30}^{\circ }.$

So the angles are :

$x={30}^{\circ }$,

$3x=3\times {30}^{\circ }={90}^{\circ }$

and $2x=2\times {30}^{\circ }={60}^{\circ }$.

Therefore, the difference between the greatest and the smallest angle $={90}^{\circ }-{30}^{\circ }={60}^{\circ }$.

Hence, option $C$ is correct.