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
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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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