Предмет: Геометрия, автор: Vill13

Найдите углы треугольника АВС, если угол А на 60 градусов мень ше угла В и в два раза и меньше угла С.

пожалуйста напишете решение!!))

Ответы

Автор ответа: kristina57
0
Сумма углов в треугольника равна 180 градусам. 
А + В + С = 180 градусов 

Угол В = (А + 60) градусов 
Угол С = (2*А) градусов 

А + (А + 60) + 2*А = 180 градусов 

Раскрываем скобки: 
А + А + 60 + 2*А = 180 
2*А + 60 + 2*А = 180 
4*А + 60 = 180 

Переносим известные слагаемые в одну строну, неизвестные оставляем: 
4*А = (180 - 60) 
4*А = 120 
А = (120/4) 
А = 30 градусов 

Проверка: 
Угол А = 30 градусов 
Угол В = 30 + 60 = 90 градусов 
Угол С = 2*30 = 60 градусов 
30 + 90 + 60 = 180 градусов 

Ответ: угол А = 30 градусов, угол В = 90 градусов, угол С = 60 градусов. 
Скорее всего в задаче надо найти не один угол, а все
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