Question

如图4.4-11,已知角AOB是直角,OM平分角BOC,ON平分角AOC,求角MON的度数.

Answer 1

分三种情况
(1) OC 在 OA,OB之间
∵ OM平分角BOC
∴ ∠COM = 1/2 ∠BOC
∵ ON平分角AOC
∴ ∠NOC = 1/2 ∠AOC
∴ ∠MON = ∠NOC + ∠COM
= 1/2 *(∠AOC+∠BOC)
= 1/2 ∠AOB = 45°
(2) OC 在 OA 外侧
∵ OM平分角BOC
∴ ∠COM = 1/2 ∠BOC
∵ ON平分角AOC
∴ ∠NOC = 1/2 ∠AOC
∴ ∠MON = ∠COM - ∠NOC
= 1/2 *(∠BOC - ∠AOC)
= 1/2 ∠AOB = 45°
(3) OC 在 OB外侧,道理同(2)
∠MON = ∠NOC - ∠MOC
= 1/2 *(∠AOC - ∠BOC)
= 1/2 ∠AOB = 45°
综合(1)(2)(3), 角MON的度数为 45度