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Внутренние углы треугольника в сумме дают 180 градусов. Внешний угол любого внутреннего угла А равен 180 - А, то есть равен сумме двух других углов В + С. Получаем такие равенства: { A + B + C = 180 { B + C = 2x { A + C = 5x { A + B = 8x Если сложить три последних равенства, то получим 2A + 2B + 2C = 2x + 5x + 8x 2(A + B + C) = 15x 2*180 = 15x x = 24 2x = 48, 5x = 120, 8x = 192 Проверим, углы треугольника A = 180 - (B + C) = 180 - 48 = 132 B = 180 - (A + C) = 180 - 120 = 60 C = 180 - (A + B) = 180 - 192 = -12 A + B + C = 132+60-12=180
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Внешний угол любого внутреннего угла А равен 180 - А, то есть равен сумме двух других углов В + С.
Получаем такие равенства:
{ A + B + C = 180
{ B + C = 2x
{ A + C = 5x
{ A + B = 8x
Если сложить три последних равенства, то получим
2A + 2B + 2C = 2x + 5x + 8x
2(A + B + C) = 15x
2*180 = 15x
x = 24
2x = 48, 5x = 120, 8x = 192
Проверим, углы треугольника
A = 180 - (B + C) = 180 - 48 = 132
B = 180 - (A + C) = 180 - 120 = 60
C = 180 - (A + B) = 180 - 192 = -12
A + B + C = 132+60-12=180