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°.