Решебник по геометрии 7 класс Мерзляк Задание 98

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

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

\[1)\ \angle a = 17\angle b:\]

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

\[17\angle b + \angle b = 180{^\circ}\]

\[18\angle b = 180{^\circ}\]

\[\angle b = 10{^\circ}.\]

\[\angle a = 17 \bullet 10{^\circ} = 170{^\circ}.\]

\[Ответ:\ \ 170{^\circ};\ 10{^\circ}.\]

\[2)\ \angle a\ :\angle b = 19\ :26;\]

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

\[\frac{19}{26}\angle b + \angle b = 180{^\circ}\]

\[19\angle b + 26\angle b = 4680{^\circ}\]

\[45\angle b = 4680{^\circ}\]

\[\angle b = 104{^\circ}.\]

\[\angle a = \frac{19}{26} \bullet 104{^\circ} = 76{^\circ}.\]

\[Ответ:\ \ 76{^\circ};\ 104{^\circ}.\]