Maths Question

(1) 設角A = x度, 角B = y度
2y = 5x
x = 0.4y
角C = 180 – x – y
= 180 – 0.4y – y
= 180 – 1.4y
角B >= 角C >= 角A
y >= 180 – 1.4y >= 0.4y
y >= 180 – 1.4y
2.4y >= 180
y >= 75
180 – 1.4y >= 0.4y
180 >= 1.8y
100 >= y
m = 100 and n = 75
m度 + n度 = 175度
(2) 設最大角為x, 最小角為y,中間角為z
中間角 z = 180 – x – y …(1)
x – y = 30
x = 30 + y … (2)
x >= z >= y …(3)
(1), (2), (3) => 30 + y >= 180 – (30 + y) – y >= y
30 + y >= 180 – 30 – 2y
3y >= 120
y >= 40 … (4)
180 – (30 + y) – y >= y
150 – 2y >= y
50 >= y … (5)
50 >= y >= 40
當y = 40, x = 70, z = 70
當y = 50, x = 80, z = 50
最小角最小為40，n最大為 70 + 70 = 140
最大角最大為80，n最小為 50 + 50 = 100
100 <= n <= 140