The sum of the three angles of a triangle is $180 °$ . If the ratio of the angles be $5 : 6 : 7$ , then find each angle of the triangle.

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Solution

Finding the angles of triangle
Let the angles $= 5 x, 6 x, 7 x$
We know that sum of the angles of a triangle is $180 °$ .
$\begin{array}{rcl} 5 x + 6 x + 7 x & = & 180 ° \\ 18 x & = & 180 ° \\ x & = & \frac{180 °}{18} \\ x & = & 10 ° \end{array}$
Hence, First angle $= 5 x = 5 \times 10 = 50 °$
Second angle $= 6 x = 6 \times 10 = 60 °$
Third angle $= 7 x = 7 \times 10 = 70 °$
Therefore, the angles of triangle are $50 °, 60 °$ and $70 °$ .

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180^{\circ}

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