If AB parallel CD ,EF perpendicular CD and angle GED=126°,find angle AGE,angle GED and angle FGE

If AB parallel CD ,EF perpendicular CD and angle GED=126°,find angle

1.	If AB parallel CD ,EF perpendicular CD and angle GED=126°,find angle AGE,angle GED and angle FGE
Answer» {tex}\\angle{/tex}AGE = {tex}\\angle{/tex}GED = 126o . . . [Alternate interior angles]{tex}\\angle{/tex}GED = 126o{tex}\\therefore{/tex}\xa0{tex}\\angle{/tex}GEF + {tex}\\angle{/tex}FED = 126o{tex}\\therefore{/tex}\xa0{tex}\\angle{/tex}GEF + 90o = 126o . . . [As EF ⊥ CD {tex}\\therefore{/tex}\xa0{tex}\\angle{/tex}FED = 90o]{tex}\\therefore{/tex}{tex}\\angle{/tex}GEF = 126o – 90o = 36o{tex}\\angle{/tex}GEC + {tex}\\angle{/tex}GEF + {tex}\\angle{/tex}FED = 180o{tex}\\angle{/tex}GEC + 36o + 90o = 180o{tex}\\angle{/tex}GEC + 126o = 180o{tex}\\angle{/tex}GEC = 180o – 126o = 54o{tex}\\angle{/tex}FGE = {tex}\\angle{/tex}GEC = 54o . . . . [Alternate interior angles]