Решебник по геометрии 7 класс Мерзляк Задание 63

\[Рисунок\ в\ учебнике.\]

\[Дано:\ \ \]

\[\angle BOM = 90{^\circ};\]

\[\angle BOC = 74{^\circ};\]

\[\angle AOM = 62{^\circ}.\]

\[Найти:\]

\[\angle AOC.\]

\[Решение.\]

\[1)\ \angle BOC:\]

\[\angle BOC = \angle BOA + \angle AOC;\]

\[\angle BOA = \angle BOC - \angle AOC.\]

\[2)\ \angle AOM:\]

\[\angle AOM = \angle AOC + \angle COM;\]

\[\angle COM = \angle AOM - \angle AOC.\]

\[3)\ \angle BOM:\]

\[\angle BOM = \angle BOA + \angle AOC + \angle COM\]

\[\angle BOM = \angle BOC + \angle AOM - \angle AOC\]

\[90{^\circ} = 74{^\circ} + 62{^\circ} - \angle AOC\]

\[\angle AOC = 46{^\circ}.\]

\[Ответ:\ \ 46{^\circ}.\]