Решебник по геометрии 7 класс Мерзляк Задание 128

\[Схематический\ рисунок.\]

\[Дано:\ \ \]

\[\angle ABC = 70{^\circ};\]

\[BD\bot BA;\]

\[BF\bot BC.\]

\[Найти:\]

\[\angle DBF;\ \]

\[\angle ABF.\]

\[Решение:\]

\[1)\ \angle ABD = \angle ABC + \angle CBD\]

\[90{^\circ} = 70{^\circ} + \angle CBD\]

\[\angle CBD = 20{^\circ}.\]

\[2)\ \angle CBF = \angle CBD + \angle DBF\]

\[90{^\circ} = 20{^\circ} + \angle DBF\]

\[\angle DBF = 70{^\circ}.\]

\[3)\ \angle ABF = \angle ABD + \angle DBF\]

\[\angle ABF = 90{^\circ} + 70{^\circ} = 160{^\circ}.\]

\[Ответ:\ \ \angle DBF = 70{^\circ};\ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \angle ABF = 160{^\circ}.\]