Question

如图已知CD//AB,OE平分角AOD,OF垂直OE,角D=52度,求角BOF

Answer 1

∵CD//AB,∠D=52°

∴∠D=∠DOB=52°

∠DOA=180°-∠D=128°

又∵OE平分角AOD

∴∠EOA=∠DOE=1/2∠DOA=64°

又∵OF⊥OE

∴∠EOF=90°

∴∠DOF=∠EOF-∠DOE=90°-64°=26°

∴∠BOF=∠DOB-∠DOF=52°-26°=26°