In $Δ, ∠ A = x + 15^{o}, ∠ B = x a n d ∠ C = 2 x - 35^{o}$ . Find each angle of the triangle and then assign a special name to the triangle.

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Solution

$∠ A = x + 15$ , $∠ B = x$ , $∠ C = 2 x - 35$
$∠ A + ∠ B + ∠ C = 180$
$x + 15 + x + 2 x - 35 = 180$
$4 x - 20 = 180$
$4 x = 200$
$x = 50$
Thus, $∠ A = 50 + 15 = 65^{\circ}$
$∠ B = 50^{\circ}$
$∠ C = 2 \times 50 - 35 = 65^{\circ}$
Since, two of the angles are equal. Hence, it is an isosceles triangle.

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Δ, ∠ A = 2 x + 15^{o}, ∠ B = 3 x - 5^{o} a n d ∠ C = 4 x + 35^{o}

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