In a ∆ABC, ∠A = x°, ∠B = (3x − 2)°, ∠C = y°. Also, ∠C − ∠B = 9°. Find the three angles.

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Solution

Let , and

$∠ C - ∠ B = 9^{°} \Rightarrow ∠ C = 9^{°} + ∠ B \Rightarrow ∠ C = 9^{°} + 3 x^{°} - 2^{°} \Rightarrow ∠ C = 7^{°} + 3 x^{°}$

Substitute in above equation we get ,

$y^{°} = 7^{°} + 3 x^{°}$

$∠ A + ∠ B + ∠ C = 180 ° \Rightarrow x^{°} + (3 x^{°} - 2^{°}) + (7^{°} + 3 x^{°}) = 180^{°} \Rightarrow 7 x^{°} + 5^{°} = 180^{°} \Rightarrow 7 x^{°} = 180^{°} - 5^{°} = 175^{°} \Rightarrow x^{\circ} = \frac{175^{\circ}}{7^{\circ}} = 25^{\circ} ∠ A = x^{\circ} = 25^{\circ} ∠ B = (3 x - 2)^{\circ} = 3 (25^{\circ}) - 2^{\circ} = 73^{\circ} ∠ C = (7^{°} + 3 x^{°}) = 7^{\circ} + 3 (25)^{\circ} = 82^{\circ} ∠ A = 25^{\circ}, ∠ B = 73^{\circ}, ∠ C = 82^{\circ} Hence, the answer .$

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