Question

如图,在Rt△ABC中,∠C＝90°,∠CAB,∠CBA的平分线AD,BE交于点F,求∠AF的读数

Answer 1

∵AD,BE分别平分∠CAB,∠CBA

∴∠FBA=1/2∠CBA

∠FAB=1/2∠CAB

∴∠FBA+∠FAB=1/2(∠CBA+∠CAB)

∵△ABC是Rt△

∴∠CAB+∠CBA=90°

∴∠FBA+∠FAB=1/2×90°=45°

∴∠AFB=180°-(∠FBA+∠FAB)=180°-45°=135°