Решебник по геометрии 9 класс Мерзляк Задание 186

\[1)\ \beta = 90{^\circ}:\]

\[\alpha = 180{^\circ} - 90{^\circ} = 90{^\circ};\]

\[S_{n} = (n - 2) \bullet 180{^\circ} = n \bullet 90{^\circ}\]

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

\[\frac{1}{2}n = 2\ \ \]

\[n = 4\ стороны.\]

\[Ответ:\ \ 4.\]

\[2)\ \beta = 24{^\circ}:\]

\[\alpha = 180{^\circ} - 24{^\circ} = 156{^\circ};\]

\[S_{n} = (n - 2) \bullet 180{^\circ} = n \bullet 156{^\circ}\]

\[n - 2 = \frac{13}{15}\text{n\ \ }\]

\[\frac{2}{15}n = 2\ \ \]

\[n = 15\ сторон.\]

\[Ответ:\ \ 15.\]