Question

1.如图已知AB∥A'D,∠B=40°∠D=35°求∠BCD的度数2.如图已知AB,CD相交于点A,且∠A=30°∠B=

Answer 1

过点C作EF∥AB 延长BC交AD于点E

∴∠B=∠BCF ∵∠A=30°,∠B=40°

∵∠B=40° ∴∠AEB=110°

∴∠BCF=40° ∵∠AEB+∠CED=180°

∵AB∥A'D ∴∠CED=70°

∴EF∥A'D ∵∠D+∠CED+∠DCE=180°,∠D=35°

∴∠DCF=∠D ∴∠DCE=75°

∵∠D=35° ∵∠DCE+∠BCD=180°

∴∠DCF=35° ∴∠BCD=105°

∴∠BCD=75°