Решебник по геометрии 7 класс Мерзляк Задание 123

\[Рисунок\ в\ учебнике.\]

\[Дано:\ \ \]

\[AB\bot CD;\ \]

\[\angle COK = 42{^\circ};\]

\[\angle MOC + \angle BOK = 130{^\circ}.\]

\[Найти:\]

\[1)\ \angle MOK;\]

\[2)\ \angle MOD.\]

\[Решение.\]

\[180{^\circ} = \angle AOM + 130{^\circ} + 42{^\circ}\ \ \]

\[\angle AOM = 8{^\circ}.\]

\[\angle AOC = \angle AOM + \angle MOC\]

\[90{^\circ} = 8{^\circ} + \angle MOC\]

\[\angle MOC = 82{^\circ}.\]

\[1)\ \angle MOK = \angle MOC + \angle COK\]

\[\angle MOK = 82{^\circ} + 42{^\circ} = 124{^\circ}.\]

\[2)\ \angle MOD = \angle AOM + \angle AOD\]

\[\angle MOD = 8{^\circ} + 90{^\circ} = 98{^\circ}.\]

\(Ответ:\ \ 1)\ 124{^\circ};\ 2)\ 98{^\circ}.\)