Решебник по геометрии 9 класс Мерзляк Задание 187

\[1)\ \beta = 120{^\circ}:\]

\[\alpha = 180{^\circ} - 120{^\circ} = 60{^\circ};\]

\[S_{n} = (n - 2) \bullet 180{^\circ} = n \bullet 60{^\circ}\]

\[n - 2 = \frac{1}{3}\text{n\ \ \ }\]

\[\frac{2}{3}n = 2\ \ \ \]

\[n = 3\ стороны.\]

\[Ответ:\ \ 3.\]

\[2)\ \beta = 72{^\circ}:\]

\[\alpha = 180{^\circ} - 72{^\circ} = 108{^\circ};\]

\[S_{n} = (n - 2) \bullet 180{^\circ} = n \bullet 108{^\circ}\]

\[n - 2 = \frac{3}{5}\text{n\ }\]

\[\frac{2}{5}n = 2\ \ \]

\[n = 5\ сторон.\]

\[Ответ:\ \ 5.\]