Triangle angles

In a triangle, ABC, the interior angle at vertex C is twice the internal angle at point A. The outer angle at point B measured 117 degrees. How big is the external angle at vertex A?

Correct answer:

A =  141 °

Step-by-step explanation:

$$\begin{gathered} \alpha +\beta +\gamma =180 \\ \gamma =2\alpha \\ 180-\beta =117 \\ \beta =180-117=63{}^{\circ } \\ \alpha +\beta +(2\cdot \alpha )=180 \\ \alpha +63+(2\cdot \alpha )=180 \\ 3\alpha =117 \\ \alpha =\frac{117}{3}=39 \\ \alpha =39 \\ \gamma =2\cdot \alpha =2\cdot 39=78{}^{\circ } \\ A=180-\alpha =180-39=141^{\circ } \end{gathered}$$

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