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प्रश्न
In ∆ABC, if ∠B is 3 times ∠A and ∠C is 2 times ∠A, then find the angle
उत्तर
In ABC, Let ∠A = x,
then ∠B = 3 times ∠A = 3x
∠C = 2 times ∠A = 2x
By angle sum property of a triangle,
Sum of three angles of ∆ABC = 180°
∠A + ∠B + ∠C = 180°
x + 3x + 2x = 180°
x(1 + 3 + 2) = 180°
6x = 180°
x = `(180^circ)/6` = 30°
∠A = x = 30°
∠B = 3x = 3 × 30° = 90°
∠C = 2x = 2 × 30° = 60°
∴ ∠A = 30°
∠B = 90°
∠C = 60°
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