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In fig., if AB।। CD, EF is perpendicular to CD and/_GED=126*, find /_AGE, /_GEF and/_FGE. |
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Answer» :- GIVEN :- AB | | CD EF is perpendicular to CD ∠GED = 126° Required to find :- ∠AGE ∠GEF ∠FGE Solution :- Given that :- AB | | CD EF is perpendicular to CD ∠GED = 126° CONSIDER,AB | | CD GE is the transversal So,∠GED = ∠AGE ( Alternate interior angles ) Hence∠AGE = 126° Similarly, ∠GEF + ∠FED = ∠GEDSo,∠GEF = ∠GED - ∠FED ∠GEF = 120° - ∠FED Since EF is perpendicular to CD ∠FED = 90°Hence,∠GEF = 120° - 90° ∠GEF = 30° Now consider ∆ GEF In ∆ GEF ∠FGE+ ∠GEF + ∠GFE = 180° ∠FGE + 30° + ∠GFE = 180° Since, EF is perpendicular to CD ∠GFE = 90° So,∠FGE + 30° + 90° = 180° ∠FGE + 120° = 180° ∠FGE = 180° - 120° ∠FGE = 60° Therefore,∠AGE = 126° ∠GEF = 30° ∠FGE = 60° |
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