In Figure, if AB\(||\)CD, EF\(⊥\)CD and \(∠ \)GED=126°, find \(∠ \)AGE,\(∠ \)GEF and \(∠ \)FGE.
Solution and Explanation
It is given that, AB \(||\) CD.
EF \(⊥\) CD
\(∠\)GED = 126º
\(⇒\) ∠GEF + \(∠\)FED = 126º
\(⇒\) \(∠\)GEF + 90º = 126º
\(⇒\) \(∠\)GEF = 36º
\(∠\)AGE and \(∠\)GED are alternate interior angles.
\(⇒\) \(∠\)AGE = \(∠\)GED = 126º
However, \(∠\)AGE + \(∠\)FGE = 180º (Linear pair)
\(⇒\) 126º + \(∠\)FGE = 180º
\(⇒\)\(∠\)FGE = 180º − 126º = 54º
∴ \(∠\)AGE = 126º, \(∠\)GEF = 36º, \(∠\)FGE = 54º
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