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

Question:

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

(a) 60°            

(b) 40°              

(c) 80°                  

(d) 20°

Thinking Process

Use the concept, the sum of all angles in a triangle is 180°. Further, simplify it and get the smallest angle.

Solution:

(b) Given, the ratio of angles of a triangle is 2 : 4 : 3.

Let the angles of a triangle be ∠A, ∠B and ∠C.

∠A = 2x, ∠B = 4x

∠C = 3x , ∠A+∠B+ ∠C= 180°

[sum of all the angles of a triangle is 180°]

2x + 4x + 3x = 180°

9x = 180°

x=180°/9 =20°

∠A=2x=2 x 20° = 40°

∠B = 4x = 4 x 20° = 80°

∠C = 3x = 3 x 20° = 60°

Hence, the smallest angle of a triangle is 40°.

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