Q13 of 50 Page 6

In Fig., if AB || CD, EF ⊥ CD and∠ GED = 126°, find ∠ AGE, ∠ GEF and ∠ FGE.

Given: AB || CD, EF perpendicular CD, ∠GED = 126o


Now, according to the question,


∠FED = 90o (EF perpendicular CD)


Now,


∠AGE = ∠GED (Since, AB parallel CD and GE is transversal, hence alternate interior angles)


Therefore,


∠AGE = 126o


And,


∠GEF = ∠GED - ∠FED


∠GEF = 126o – 90o


∠GEF = 36o


Now,


∠FGE + ∠AGE = 180o (Linear pair)


∠FGE – 180o – 126o


∠FGE = 54o


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