Angles in triangle

The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?

Correct result:

β =  82 °
γ =  42 °
α =  56 °

Solution:

$$\begin{gathered} \alpha +\beta +\gamma =180^{\circ } \\ \beta \mathrm{/}\gamma =6\mathrm{/}8 \\ \alpha =40^{\circ }+\beta \\ \alpha ={\displaystyle \frac{6\cdot {\displaystyle \frac{180-40}{{\displaystyle \frac{2\cdot 6}{8}}+1}}}{8}}+40=82^{\circ } \end{gathered}$$

$\beta ={\displaystyle \frac{6\cdot {\displaystyle \frac{180-40}{{\displaystyle \frac{2\cdot 6}{8}}+1}}}{8}}=42^{\circ }$

$\gamma ={\displaystyle \frac{180-40}{{\displaystyle \frac{2\cdot 6}{8}}+1}}=56^{\circ }$

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