ГДЗ по геометрии 7 класс Атанасян Задание 1083

\[\boxed{\mathbf{1083.ОК\ ГДЗ - домашка\ на}\ 5}\]

\[Внутренние\ углы\ правильного\ \]

\[n - угольника\ находятся\ по\ \]

\[формуле:\]

\[\alpha = \frac{n - 2}{n} \bullet 180{^\circ}.\]

\[Отсюда:\ \]

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

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

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

\[360{^\circ} = n(180{^\circ} - \alpha)\]

\[n = \frac{360{^\circ}}{180{^\circ} - \alpha}.\]

\[\textbf{а)}\ \alpha = 60{^\circ}:\ \ \ \]

\[n = \frac{360{^\circ}}{180{^\circ} - 60{^\circ}} = \frac{360{^\circ}}{120{^\circ}} = 3;\]

\[\textbf{б)}\ \alpha = 90{^\circ}:\ \ \ \]

\[n = \frac{360{^\circ}}{180{^\circ} - 90{^\circ}} = \frac{360{^\circ}}{90{^\circ}} = 4;\]

\[\textbf{в)}\ \alpha = 135{^\circ}:\ \ \ \]

\[n = \frac{360{^\circ}}{180{^\circ} - 135{^\circ}} = \frac{360{^\circ}}{45{^\circ}} = 8;\]

\[\textbf{г)}\ \alpha = 150{^\circ}:\ \ \ \]

\[n = \frac{360{^\circ}}{180{^\circ} - 150{^\circ}} = \frac{360{^\circ}}{30{^\circ}} = 12.\]