In $Δ, ∠ A = 2 x + 15^{o}, ∠ B = 3 x - 5^{o} a n d ∠ C = 4 x + 35^{o}$ . Find the difference of largest and smallest triangle of triangle ( in degrees )

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Solution

$∠ A = 2 x + 15$ , $∠ B = 3 x - 5$ , $∠ C = 4 x + 35$
$∠ A + ∠ B + ∠ C = 180$
$2 x + 15 + 3 x - 5 + 4 x + 35 = 180$
$9 x + 45 = 180$
$9 x = 135$
$x = 15$
Thus, $∠ A = 2 \times 15 + 15 = 45^{\circ}$
$∠ B = 3 \times 15 - 5 = 40^{\circ}$
$∠ C = 4 \times 15 + 35 = 95^{\circ}$
Difference = $95^{\circ} - 40^{\circ} = 55^{\circ}$

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