Magnitude 29891

The triangle ABC is the magnitude of the inner angle α 12 ° smaller than the angle β, and the angle γ is four times larger than the angle α. What size are these interior angles in the triangle?

Final Answer:

α =  28 °
β =  40 °
γ =  112 °

Step-by-step explanation:

$$\begin{gathered} \alpha =\beta -12 \\ \gamma =4\cdot \alpha \\ \alpha +\beta +\gamma =180 \\ (\beta -12)+\beta +4\cdot \alpha =180 \\ (\beta -12)+\beta +4\cdot (\beta -12)=180 \\ 6\beta =240 \\ \beta =\frac{240}{6}=40 \\ \beta =40 \\ \alpha =\beta -12=40-12=28^{\circ } \end{gathered}$$

$\gamma =4\cdot \alpha =4\cdot 28=112^{\circ }$

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