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Question
Angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is ______.
Options
60°
40°
80°
20°
Solution
Angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is 40°.
Explanation:
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 and ∠C = 3x ,
∠A + ∠B + ∠C = 180° ...[Sum of all the angles of a triangle is 180°]
2x + 4x + 3x = 180°
9x = 180°
x =
∠A = 2x = 2 × 20° = 40°
∠B = 4x = 4 × 20° = 80°
∠C = 3x = 3 × 20° = 60°
Hence, the smallest angle of a triangle is 40°.
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