Question

The angles of a triangle are in the ratio 2: 1: 3. Is the triangle right-angled triangle?

• A. True
• B. False

Answer 1

The correct option is A True

The angles of the triangle are in the ratio, $2:1:3$.
Let the angles be $2x,x$ and $3x$.

By angle sum property, sum of the angles $={180}^o$
$2x+x+3x={180}^o$
$⟹$ $6x={180}^o$
$⟹$ $x={30}^o$ .

Hence, the angles will be $x={30}^o,2x={60}^o$ and $3x={90}^o$.

Since, one of the angles is ${90}^o$, the triangle is a right angled triangle.

Hence, the statement is true and option $A$ is correct.