The angle of a triangle are $(2 x)^{o}, (3 x + 5)^{o}$ and $(4 x - 14)^{o}$ .
Find the value of x and the measure of each angle of the triangle.

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Solution

We know that the sum of the angles of a triangle is 180 $^{o}$ .
$∴ 2 x^{o} + 3 x^{o} + 5^{o} + 4 x^{o} - 14^{o} = 180^{o} \Rightarrow 9 x^{o} - 9^{o} = 180^{o}$
$\Rightarrow 9 x^{o} = 180^{o} + 9^{o} = 189^{o}$
$\Rightarrow x = \frac{189^{o}}{9^{o}} = 21$
$∴ 2 x^{o} = (2 \times 21)^{o} = 42^{o}, (3 x + 5)^{o} = [(3 \times 21 + 5)]^{o} = 68^{o}$
$(4 x - 14)^{o} = [(4 \times 21) - 14]^{o} = 70^{o}$
Hence, the angles of the triangle are $24^{o}$ , $68^{o}$ and $70^{o}$ .

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