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

Question

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

cdquestions Admin · Accepted Answer

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

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

In Figure, if AB\(||\)CD, EF\(⊥\)CD and \(∠ \)GED=126°, find \(∠ \)AGE,\(∠ \)GEF and \(∠ \)FGE.

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions