Решение задачи 58: Найти x

Задание 58. Найдите \(x\). Для решения всех задач используется теорема о сумме углов треугольника: сумма углов любого треугольника равна \(180^{\circ}\). 2) \(x + 85^{\circ} + 60^{\circ} = 180^{\circ}\) \(x = 180^{\circ} - (85^{\circ} + 60^{\circ}) = 180^{\circ} - 145^{\circ} = 35^{\circ}\) Ответ: \(x = 35^{\circ}\). 3) \(x + 45^{\circ} + 65^{\circ} = 180^{\circ}\) \(x = 180^{\circ} - (45^{\circ} + 65^{\circ}) = 180^{\circ} - 110^{\circ} = 70^{\circ}\) Ответ: \(x = 70^{\circ}\). 4) \(x + 53^{\circ} + 42^{\circ} = 180^{\circ}\) \(x = 180^{\circ} - (53^{\circ} + 42^{\circ}) = 180^{\circ} - 95^{\circ} = 85^{\circ}\) Ответ: \(x = 85^{\circ}\). 5) \(x + 30^{\circ} + 20^{\circ} = 180^{\circ}\) \(x = 180^{\circ} - (30^{\circ} + 20^{\circ}) = 180^{\circ} - 50^{\circ} = 130^{\circ}\) Ответ: \(x = 130^{\circ}\). 6) \(x + 100^{\circ} + 45^{\circ} = 180^{\circ}\) \(x = 180^{\circ} - (100^{\circ} + 45^{\circ}) = 180^{\circ} - 145^{\circ} = 35^{\circ}\) Ответ: \(x = 35^{\circ}\). 7) \(x + 21^{\circ} + 50^{\circ} = 180^{\circ}\) \(x = 180^{\circ} - (21^{\circ} + 50^{\circ}) = 180^{\circ} - 71^{\circ} = 109^{\circ}\) Ответ: \(x = 109^{\circ}\). 8) \(x + 128^{\circ} + 19^{\circ} = 180^{\circ}\) \(x = 180^{\circ} - (128^{\circ} + 19^{\circ}) = 180^{\circ} - 147^{\circ} = 33^{\circ}\) Ответ: \(x = 33^{\circ}\). 9) В прямоугольном треугольнике один угол равен \(90^{\circ}\). \(x + 90^{\circ} + 60^{\circ} = 180^{\circ}\) \(x = 180^{\circ} - 150^{\circ} = 30^{\circ}\) Ответ: \(x = 30^{\circ}\). 10) \(x + 90^{\circ} + 70^{\circ} = 180^{\circ}\) \(x = 180^{\circ} - 160^{\circ} = 20^{\circ}\) Ответ: \(x = 20^{\circ}\). 11) \(x + 90^{\circ} + 53^{\circ} = 180^{\circ}\) \(x = 180^{\circ} - 143^{\circ} = 37^{\circ}\) Ответ: \(x = 37^{\circ}\). 12) \(x + 90^{\circ} + 31^{\circ} = 180^{\circ}\) \(x = 180^{\circ} - 121^{\circ} = 59^{\circ}\) Ответ: \(x = 59^{\circ}\).