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

Right-angle triangle

Let 1st angle be x

⇒ 2nd angle = 2x

⇒ 3rd angle = 3x

Now,

⇒ Sum of angles = 180

⇒ x + 2x + 3x = 180

⇒ 6x = 180

⇒ x = \({30}^\circ\)

Angles will be

⇒ 1st angle = x = \({30}^\circ\)

⇒ 2nd angle = 2x = 2 x 30 = \({60}^\circ\)

⇒ 3rd angle = 3x = 3 x 30 = \({90}^\circ\)

As one of the angles is \({90}^\circ\), therefore it is a right angled triangle.