In a $△ A B C, ∠ A = x, ∠ B = (3 x - 2), ∠ C = y$ . Also, $∠ C - ∠ B = 9$ . Find the three angles.

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Solution

$I n a △ A B C,$ (By angle sum property)
$∠ A + ∠ B + ∠ C = 180^{\circ}$
$∠ C - ∠ B = 9$

$⟹ y - (3 x - 2) = 9$
$∴ y = 7 + 3 x$
$x + (3 x - 2) + y = 180^{\circ}$

$⟹ 4 x - 2 + 7 + 3 x = 180^{\circ}$
$⟹ x = 25^{\circ}$
$∴ y = 7 + 3 \times 25 = 82^{\circ}$
$∴ ∠ A = x = 25^{\circ}, B = 3 x - 2 = 73^{\circ}$

$∠ C = y = 82^{\circ}$

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Similar questions

∆ A B C, ∠ A = x^{\circ}, ∠ B = {(3 x - 2)}^{\circ}, ∠ C = y^{\circ} and ∠ C - ∠ B = 9^{\circ} .

A B C, ∠ A = x^{\circ}, ∠ B = (3 x - 2)^{\circ}

∠ C = y^{\circ}

∠ C - ∠ B = 9^{\circ}

Δ A B C

In a $△ A B C, ∠ A = x^{\circ}, ∠ B = (3 x - 2)^{\circ}, ∠ C = y^{\circ} a n d ∠ C - ∠ B = 9^{\circ}$ .Find the three angles.

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