\[\boxed{\mathbf{1083.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Внутренние\ углы\ правильного\ \]
\[n - угольника\ находятся\ по\ \]
\[формуле:\]
\[\alpha = \frac{n - 2}{n} \bullet 180{^\circ}.\]
\[Отсюда:\ \]
\[\alpha n = (n - 2)180{^\circ}\]
\[\alpha n = 180{^\circ}n - 360{^\circ}\]
\[360{^\circ} = 180{^\circ}n - \alpha n\]
\[360{^\circ} = n(180{^\circ} - \alpha)\]
\[n = \frac{360{^\circ}}{180{^\circ} - \alpha}.\]
\[\textbf{а)}\ \alpha = 60{^\circ}:\ \ \ \]
\[n = \frac{360{^\circ}}{180{^\circ} - 60{^\circ}} = \frac{360{^\circ}}{120{^\circ}} = 3;\]
\[\textbf{б)}\ \alpha = 90{^\circ}:\ \ \ \]
\[n = \frac{360{^\circ}}{180{^\circ} - 90{^\circ}} = \frac{360{^\circ}}{90{^\circ}} = 4;\]
\[\textbf{в)}\ \alpha = 135{^\circ}:\ \ \ \]
\[n = \frac{360{^\circ}}{180{^\circ} - 135{^\circ}} = \frac{360{^\circ}}{45{^\circ}} = 8;\]
\[\textbf{г)}\ \alpha = 150{^\circ}:\ \ \ \]
\[n = \frac{360{^\circ}}{180{^\circ} - 150{^\circ}} = \frac{360{^\circ}}{30{^\circ}} = 12.\]
\[\boxed{\mathbf{1083.еуроки - ответы\ на\ пятёрку}}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\mathrm{\Delta}ABC;\]
\[A( - 5;13);B(3;5);\]
\[C( - 3; - 1);\]
\[M,N,K - середины\ сторон.\]
\[\mathbf{Найти:}\]
\[\textbf{а)}\ координаты - \ M,N\ и\ K;\]
\[\textbf{б)}\ BK;\]
\[\textbf{в)}\ MN;MK;NK.\]
\[\mathbf{Решение.}\]
\[\textbf{б)}\ BK = \sqrt{(3 + 4)^{2} + (5 - 6)^{2}} =\]
\[= \sqrt{50} = 5\sqrt{2}.\]
\[\textbf{в)}\ 1)\ MN =\]
\[= \sqrt{( - 1 - 0)^{2} + (9 - 2)^{2}} =\]
\[= \sqrt{50} = 5\sqrt{2};\]
\[2)\ MK =\]
\[= \sqrt{( - 1 + 4)^{2} + (9 - 6)^{2}} =\]
\[= \sqrt{18} = 3\sqrt{2};\]
\[3)\ NK = \sqrt{(0 + 4)^{2} + (2 - 6)^{2}} =\]
\[= \sqrt{32} = 4\sqrt{2}.\]
\[Ответ:а)\ M( - 1;9);\ N(0;2);\ \]
\[K( - 4;6);\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ б)\ \ BK = \ 5\sqrt{2};\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ в)\ MN = 5\sqrt{2};\]
\(MK = 3\sqrt{2};NK = 4\sqrt{2}.\)