Alfa beta gama

The triangle's interior angle beta is 10 degrees greater than the angle alpha, and the gamma angle is three times larger than the beta. Determine the size of the interior angles.

Final Answer:

α =  28 °
β =  38 °
γ =  114 °

Step-by-step explanation:

$$\begin{gathered} \beta =\alpha +10 \\ \gamma =3\cdot \beta \\ \alpha +\beta +\gamma =180 \\ \alpha -\beta =-10 \\ 3\beta -\gamma =0 \\ \alpha +\beta +\gamma =180 \\ Row3-Row1\to Row3 \\ 2\beta +\gamma =190 \\ Row3-\frac{2}{3}\cdot Row2\to Row3 \\ 1.667\gamma =190 \\ \gamma =\frac{190}{1.66666667}=114 \\ \beta =\frac{0+\gamma }{3}=\frac{0+114}{3}=38 \\ \alpha =-10+\beta =-10+38=28=28^{\circ } \\ \alpha =28 \\ \beta =38 \\ \gamma =114 \end{gathered}$$

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