Determine 82143

Determine the size of the interior angles in an isosceles triangle if you know that the angle opposite the base is 15° greater than the angles at the base.

Final Answer:

α =  55 °
β =  55 °
γ =  70 °

Step-by-step explanation:

$$\begin{gathered} \gamma =15°+\alpha \\ \alpha =\beta \\ \alpha +\beta +\gamma =180{}^{\circ } \\ \alpha +\alpha +(15+\alpha )=180 \\ 3\alpha =165 \\ \alpha =\frac{165}{3}=55 \\ \alpha =55=55^{\circ } \end{gathered}$$

$\beta =\alpha =55=55^{\circ }$

$\gamma =15+\alpha =15+55=70^{\circ }$

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