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?

Result

β =  82 °
γ =  42 °
α =  56 °

Solution:

\alpha + \beta + \gamma = 180 ^\circ \ \\ \beta /\gamma =6/8 \ \\ \alpha = 40 ^\circ + \beta \ \\ \ \\ \alpha = \dfrac{ 6 \cdot \dfrac{180-40}{ \dfrac{2\cdot6}8+1}}8 + 40 = 82 \text{ ^\circ }
\beta = \dfrac{ 6 \cdot \dfrac{180-40}{ \dfrac{2\cdot6}8+1}}8 = 42 \text{ ^\circ }
\gamma = \dfrac{180-40}{ \dfrac{2\cdot6}8+1} = 56 \text{ ^\circ }



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