Решебник по геометрии 7 класс Мерзляк Задание 64

\[Рисунок\ в\ учебнике.\]

\[Дано:\ \ \]

\[\angle ACP = 180{^\circ};\]

\[\angle ACF = 158{^\circ};\]

\[\angle TCP = 134{^\circ}.\]

\[Найти:\]

\[\angle TCF.\]

\[Решение.\]

\[1)\ \angle TCP:\]

\[\angle TCP = \angle TCF + \angle FCP\]

\[\angle FCP = \angle TCP - \angle TCF.\]

\[2)\ \angle ACF:\]

\[\angle ACF = \angle ACT + \angle TCF\]

\[\angle ACT = \angle ACF - \angle TCF.\]

\[3)\ \angle ACP:\]

\[\angle ACP = \angle ACT + \angle TCF + \angle FCP\]

\[\angle ACP = \angle ACF + \angle TCP - \angle TCF\]

\[180{^\circ} = 158{^\circ} + 134{^\circ} - \angle TCF\]

\[\angle AOC = 112{^\circ}.\]

\[Ответ:\ \ 112{^\circ}.\]