Question

The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle is
(a) 60°
(b) 80°
(c) 76°
(d) 84°

Answer 1

(b) 80^o
Let the measures of the given angles be (2x)^o, (3x)^o​ and (4x)^o.
$\therefore$ (2x)^o + (3x)^o + (4x)^o = 180^o
⇒ (9x)^o = 180^o
​ ⇒ x = 180 / 9
⇒ x = 20^o
$\therefore$ ​2x = 40^o, 3x = 60^o, 4x = 80^o

Hence, the measures of the angles of the triangle are 40^o​, 60^o, 80^o.
Thus, the largest angle is 80^o.