Question : If the angles of a triangle are in the ratio of 1 : 2 : 3, what is the type of such triangle?
Option 1: Isosceles triangle
Option 2: Equilateral triangle
Option 3: Right-angle triangle
Option 4: Obtuse- angle triangle
Correct Answer: Right-angle triangle
Solution :
Given: the angles of a triangle are in the ratio of 1 : 2 : 3.
Let the angles be $x, 2x,$ and $3x$.
The sum of the angles of a triangle = 180°
⇒ $x+2x+3x = 180°$
⇒ $6x = 180°$
⇒ $x = 30°$
$\therefore$ The angles of the triangle are = $30°, (2\times 30°),$ and $(3\times30°) = 30°, 60°,$ and $90°$
Here one angle is 90° which means it will be a right-angle triangle.
Hence, the correct answer is the right-angle triangle.
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