如图,CB∥OA,∠B=∠A=100°,E、F在CB上,且满足∠FOC=∠AOC,OE平分∠BOF.

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  • (1)∵CB∥OA,

    ∴∠BOA+∠B=180°,

    ∵∠BOA=80°,

    ∴∠FOC=∠AOC,OE平分∠BOF,

    ∴∠EOC=∠EOF+∠FOC=

    ∠BOF+

    ∠FOA=

    (∠BOF+∠FOA)=

    ×80°=40°;

    (2)不变.

    ∵CB∥OA,

    ∴∠OCB=∠COA,∠OFB=∠FOA,

    ∵∠FOC=∠AOC,

    ∴∠COA=

    ∠FOA,即∠OCB:∠OFB=1:2.

    (3)在平行移动AC的过程中,存在∠OEB=∠OCA,且∠OCA=60°.

    设∠OCA=α,∠AOC=x,

    ∵∠OEB=∠COE+∠OCB=40°+x,

    ∠ACO=80°﹣x,

    ∴α=80°﹣x,40°+x=α,

    ∴x=20°,α=60°.