Решебник по геометрии 7 класс Мерзляк Задание 97

\[\angle a\ и\ \angle b - смежные\ углы.\]

\[Сумма\ смежных\ углов\ равна\ 180{^\circ}.\]

\[1)\ \angle a = \angle b + 70{^\circ}:\]

\[\angle a + \angle b = 180{^\circ}\]

\[\angle b + 70{^\circ} + \angle b = 180{^\circ}\]

\[2\angle b = 110{^\circ}\]

\[\angle b = 55{^\circ}.\]

\[\angle a = 55{^\circ} + 70{^\circ} = 125{^\circ}.\]

\[Ответ:\ \ 125{^\circ};\ 55{^\circ}.\]

\[2)\ \angle b = 8\angle a:\]

\[\angle a + \angle b = 180{^\circ}\]

\[\angle b + 8\angle b = 1440{^\circ}\]

\[9\angle b = 1440{^\circ}\]

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

\[\angle a = \frac{160{^\circ}}{8} = 20{^\circ}.\]

\[Ответ:\ \ 20{^\circ};\ 160{^\circ}.\]

\[3)\ \angle a\ :\angle b = 3\ :2\]

\[\angle a + \angle b = 180{^\circ}\]

\[\frac{3}{2}\angle b + \angle b = 180{^\circ}\]

\[3\angle b + 2\angle b = 360{^\circ}\]

\[5\angle b = 360{^\circ}\]

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

\[\angle a = \frac{3}{2} \bullet 72{^\circ} = 108{^\circ}.\]

\[Ответ:\ \ 108{^\circ};\ 72{^\circ}.\]