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

Question:

The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle of the triangle is
(a) 12°
(b) 100°
(c) 80°
(d) 60°

Solution:

Suppose ∆ABC be such that ∠A : ∠B : ∠C = 2 : 3 : 4.

Let ∠A = 2k, ∠B = 3and ∠C = 4k, where k is some constant.

In ∆ABC,

∠A + ∠B + ∠C = 180º      (Angle sum property)

⇒ 2k + 3k + 4k = 180º

⇒ 9k = 180º

⇒ k = 20º

∴ Measure of the largest angle = 4k = 4 × 20º = 80º

Hence, the correct answer is option (c).

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