Question

The angle of a triangle are in the ratio 2 : 3 : 4. The largest angle of the triangle is

(a) ${120}^{\circ }$

(b) ${100}^{\circ }$

(c) ${80}^{\circ }$

(d) ${60}^{\circ }$

Answer 1

ANSWER:
Suppose ∆ABC be such that ∠A : ∠B : ∠C = 2 : 3 : 4.
Let ∠A = 2k , ∠B = 3k and ∠C = 4k , where k is some constant.
In ∆ABC,
$\angle A+\angle B+\angle C={180}^{\circ }$
(Angle sum property)
⇒$2k+3k+4k={180}^{\circ }$
⇒ $9k={180}^{\circ }$
⇒$k={20}^{\circ }$
∴ Measure of the largest angle =$4k=4\times {20}^{\circ }={80}^{\circ }$
Hence, the correct answer is option (c).