Question

如图，AB//EF，角C=90度，求角ABC，角CDE，角DEF之间的关系，并证明

在线急等!!!

Answer 1

∠CDE=90°+∠DEF-∠ABC
过点C、D分别作AB的平行线CM、DN
AB//EF
AB//EF‖CM‖DN
∠ABC=∠BCM
∠MCD=∠CDN
∠NDE=∠DEF
∠CDE=∠CDN+∠NDE
=∠MCD+∠DEF
=∠BCD-∠BCM+∠DEF
=90°-∠ABC+∠DEF

Answer 2

∠DEF+90°=∠ABC+∠CDE

过程：延长CD交EF于M，交AB于N，
∠BNC=∠DME=90°-∠ABC
∠EDM=180°-∠CDE
在△DEM中，内角和为180°
∠EDM+∠DME+∠DEF=180°-∠CDE+90°-∠ABC+∠DEF=180°

Answer 3

∠ABC+∠CDE-∠DEF=90°