Question

The angles of a triangle are in the ratio $1:2:3$ the triangle is

• A. right-angled
• B. scalene
• C. isosceles
• D. equilateral

Answer 1

The correct option is A

right-angled

Correct option:(a) right-angled

Given the angles of a triangle are in the ratio $1:2:3$

Let $\angle A,\angle Band\angle C$ are the angles of $△ABC$

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

then for any value of $x$

$\angle A=x,\angle B=2xand\angle C=3x$

By the angle sum property of triangles

$$\begin{gathered} \angle A+\angle B+\angle C=180° \\ \Rightarrow x+2x+3x=180° \\ \Rightarrow 6x=180° \\ \Rightarrow x=\frac{180°}{6}=30° \end{gathered}$$

Thus,

$$\begin{gathered} \angle A=x=30° \\ \angle B=2x=2\times 30°=60° \\ \angle C=3x=3\times 30°=90° \end{gathered}$$

So, this is a right-angled triangle because one angle is $90°$

Incorrect options:

(b)scalene

Since the given triangle has a right angle. Therefore this is right-angled.

So, this option is incorrect.

(b)isosceles

Since the given triangle has a right angle and also its two angles are not equal. Therefore this is right-angled.

So, this option is incorrect.

(b)equilateral

Since the given triangle has a right angle and also its all angle are not equal. Therefore this is right-angled.

So, this option is incorrect.

Hence, option (a) is correct.