Question

The angles of a triangle are in the ratio 2:3 : 4. The largest angle of the
triangle is
(a) 120°
(b) 100°
(c) 80°
(d) 60°​

Answer 1

AnswEr :

The largest angle of the triangle is 80° (option C) .

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GiveN :

Angles of the triangle are in the ratio 2 : 3 : 4

To FinD :

Largest angle of the triangle = ?

SoluTion :

Let's assume the values of angles as,

∠A = 2x

∠B = 3x

∠C = 4x

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Now, We know that the sum of all the angles of a triangle is 180°(Angle sum property).

So, in any ΔABC

∠A + ∠B + ∠C = 180°

Substituting the values as per our assumption,

➠ 2x + 3x + 4x = 180°

➠ 9x = 180°

➠ x = 180°/9

➠ x = 20°

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★ So, the angles are :

∠A = 2x = 2(20) = 40°

∠B = 3x = 3(20) = 60°

∠C = 4x = 4(20) = 80°

∴ The largest angle is 80°

Hope it helps.

Answer 2

Answer :-

80°

Given :-

• Angles of a traingle are in the ratio 2:3:4

To Find :-

• largest angle of the traingle.

Solution :-

Put x in the ratio

Then,

2x + 3x + 4x = 180 [ angle sum property of a ∆ ]

=> 9x = 180

=> x = 180/9

=> x = 20

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=> 2x = 2 × 20 = 40°

=> 3x = 3 × 20 = 60°

=> 4x = 4 × 20 = 80°

The largest angle of the traingle is 80°

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