Question

If angles in a triangle are in the ratio 1:2:3, then what is the type of triangle?

• A. Isosceles right angled triangle
• B. Right angled triangle
• C. Acute angled triangle
• D. Obtuse angled triangle

Answer 1

The correct option is B Right angled triangle

Let the triangle be $ABC$.

By given data, angles in $\Delta ABC$ are in ratio 1 : 2 : 3.
Let us assume $\angle A$ be the smallest angle and $\angle C$ be the greatest angle.

$\angle A:\angle B:\angle C=1:2:3$

We Know that,
$\angle A+\angle B+\angle C={180}^{\circ }\cdot \cdot \cdot \left(i\right)$ [Angle Sum Property]

Let $\angle A$ = $x^{\circ }$, $\angle B$ = $2x^{\circ }$, $\angle C$ = $3x^{\circ }$

Substituting angles in equation $\left(i\right)$
$\Rightarrow$ $x^{\circ }$ + $2x^{\circ }$+$3x^{\circ }$ = ${180}^{\circ }$
$\Rightarrow 6x^{\circ }$ = ${180}^{\circ }$
$\Rightarrow x^{\circ }$ = $\frac{{180}^{\circ }}{6}$
$\Rightarrow x^{\circ }$ = ${30}^{\circ }$

Since, $\angle A$ = $x^{\circ }$, $\angle B$ = $2x^{\circ }$, $\angle C$ = $3x^{\circ }$
$\angle A={30}^{\circ }$
$\angle B=2\times {30}^{\circ }={60}^{\circ }$
$\angle C=3\times {30}^{\circ }={90}^{\circ }$
As $\angle C={90}^{\circ }$, it is a right angled triangle.