Question

Внутри угла ABC, равного 60°, проведен луч ВМ. Внутри угла АВМ проведен луч ВК,∠АВМ=50°, ∠КВС=40°. найдите угол между биссектрисами углов АВК и СВМ.

Answer 1

Ответ:

45°

Пошаговое объяснение:

∠АВС = 60°, ∠АВМ = 50°

∠АВС = ∠АВМ + ∠МВС

∠МВС = ∠АВС - ∠АВМ = 60° - 50° = 10°

ВР - биссектриса ∠МВС ⇒ ∠МВР = ∠СВР = 10° : 2 = 5°

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∠КВС = 40°

∠АВС = ∠КВС + ∠АВК

∠АВК = ∠АВС - ∠АВК = 60° - 40° = 20°

ВО - биссектриса ∠АВК ⇒ ∠АВО = ∠КОВ = 20° : 2 = 10°

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∠КВС = 40°

∠КВС = ∠КВМ + ∠МВС

∠КВМ = ∠КВС - ∠МВС = 40° - 10° = 30°

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Найдите угол между биссектрисами углов АВК и СВМ.

т.е. надо найти ∠ОВР

∠ОВР = ∠ОВК + ∠КВМ + ∠МВР = 10° + 30° + 5° = 45°