ГДЗ по геометрии 8 класс Мерзляк Задание 346

\[Схематический\ рисунок.\]

\[Дано:\]

\[O - центр\ опис.\ окружности;\]

\[AD - диаметр;\]

\[\angle ABC = 108{^\circ};\]

\[\angle BCD = 132{^\circ}.\]

\[Найти:\]

\[\angle BAD;\ \angle ADC;\]

\[\angle CAD;\ \angle BDA.\]

\[Решение\]

\[\angle BAD + \angle BCD = 180{^\circ}\]

\[\angle BAD + 132{^\circ} = 180{^\circ}\]

\[\angle BAD = 48{^\circ}.\]

\[\angle ADC + \angle ABC = 180{^\circ}\]

\[\angle ADC + 108{^\circ} = 180{^\circ}\]

\[\angle ADC = 72{^\circ}.\]

\[\cup ABC = 2\angle ADC = 144{^\circ};\]

\[\cup CD = 180{^\circ} - \cup ABC = 36{^\circ};\]

\[\angle CAD = \frac{1}{2} \cup CD = 18{^\circ};\]

\[\cup DCB = 2\angle BAD = 96{^\circ};\]

\[\cup AB = 180{^\circ} - \cup DCB = 84{^\circ};\]

\[\angle BDA = \frac{1}{2} \cup AB = 42{^\circ}.\]

\[Ответ:\ \ 48{^\circ};\ 72{^\circ};\ 18{^\circ};\ 42{^\circ}.\]