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∠ 1 = ?°, на 55° больше, чем ∠ 2.
∠ 2 = ?°
Оба угла являются смежными.
Решение:Пусть x° равен смежный ∠ 2, тогда ∠ 1 равен (55+x)˚. Зная, что свойство смежных углов всегда содержит сумму 180°, составим уравнение с переменными и решим задачу алгебраическим
Составление математической модели:
Работа с математической моделью:
Поскольку уравнение имеет переменные, раскроем скобки и найдём значение переменных:
Теперь, зная что число с переменной и число без переменной в данном случае вычислить невозможно, перенесем число без переменной в правую часть уравнения (число становится отрицательным):
Затем вычислим полученный пример, находящийся в правой части уравнения:
Чтобы найти неизвестный множитель, необходимо произведение разделить на известный множитель:
ответ математической модели:
Исходя из значения данного примера, получим корень уравнения:
Теперь остаётся только узнать величину ∠ 1:
˚ - ∠ 1.
Проверка: 117,5° + 62,5° = 180° - задача решена верно.ответ: ∠ 1 = 117,5°; ∠ 2 = 62,5°.