Question

如图,已知四边形ABCD中,DE=CE分别平分∠ADC、∠BCD,∠A=100°,∠B=92°,求∠DEC的度数

Answer 1

DE平分∠ADC

∠ADE = ∠CDE = 1/2 ∠ADC

CE平分∠BCD

∠BCE = ∠DCE = 1/2 ∠BCD

延长DE交BC于F

∠FEC =∠CDE + ∠DCE = 1/2 (∠ADC + ∠BCD) = 1/2 (360° -∠A - ∠B)

= 1/2 (360° -100 °- 92°) = 84°

∠DEC = 180° - 84° = 96°