ГДЗ по геометрии 9 класс Мерзляк Задание 204

\[\ \alpha - угол\ n\text{-}угольника;\]

\[\beta = \alpha - 36{^\circ}:\]

\[\alpha = \frac{180{^\circ} \bullet (n - 2)}{n};\ \]

\[\ \beta = \frac{360{^\circ}}{n};\]

\[\frac{360{^\circ}}{n} = \frac{180{^\circ} \bullet n - 360{^\circ}}{n} - 36{^\circ}\]

\[360{^\circ} = 180{^\circ} \bullet n - 360{^\circ} - 36{^\circ} \bullet n\]

\[144{^\circ} \bullet n = 720{^\circ}\ \ \ \]

\[n = 5\ сторон.\]

\[Ответ:\ \ 5.\]