<AKB = 180 – (A/2) – (B/2) = ((360 - (A + B))/2 = ((360 - (180 - C))/2 =
= (180 + C)/2.
AKB + C = 165 по заданию.
Заменим <AKB = (180 + C)/2.
((180 + C)/2) + С = 165.
180 + C + 2С = 2*165.
3С = 330 – 180 = 150.
С = 150/3 = 50 градусов.
Проверяем: A + B = 180 – C = 180 – 50 = 130.
(A + B)/2 = 65.
AKB = 180 – 65 = 115.
Сравним: <AKB = (180 + C)/2 = (180 + 50)/2 = 230/2 = 115.
Совпадает, решение верно.
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Answers & Comments
<AKB = 180 – (A/2) – (B/2) = ((360 - (A + B))/2 = ((360 - (180 - C))/2 =
= (180 + C)/2.
AKB + C = 165 по заданию.
Заменим <AKB = (180 + C)/2.
((180 + C)/2) + С = 165.
180 + C + 2С = 2*165.
3С = 330 – 180 = 150.
С = 150/3 = 50 градусов.
Проверяем: A + B = 180 – C = 180 – 50 = 130.
(A + B)/2 = 65.
AKB = 180 – 65 = 115.
Сравним: <AKB = (180 + C)/2 = (180 + 50)/2 = 230/2 = 115.
Совпадает, решение верно.