Question

"Question 3 In the given figure, If AB || CD, EF ⊥ CD and ∠GED = 126º, find ∠AGE, ∠GEF and ∠FGE.

Class 9 - Math - Lines and Angles Page 104"

Answer 1

Alternate angles:

When two lines are crossed by another line the pair of angles on opposite sides of the transversal is called alternate angles.

 

Theorem 1

If a transversal intersects two Parallel Lines then each pair of alternate interior angles is equal.

Theorem 2

If a transversal intersects two lines such that a pair alternate interior angle is equal then the two lines are parallel.

 

Solution:

Given:  ∠AGE=126°

∠AGE=∠GED=126∘ 

 

[alternate interior angles]

 

(ii) ∠GED=∠GEF+∠FED=126∘

⇒∠GEF+90∘=126°

(given that EF⊥CD)

 

⇒∠GEF=126°−90°=36°

(iii) ∠CEG+∠GED=180∘

 (given ∠GED=126∘)

 

⇒∠CEG+126°=180∘

 ⇒∠CEG=180∘−126∘ 

⇒∠CEG=54∘

∠FGE=∠CEG=54∘      

 (alternate angles)

 

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Hope this will help you....

Answer 2

yes
solution is here
(1) <AGE=<GED=126° ( alternate angle )
(2) <GED=126°
=> <GEF+<FED= 126°
=> <GEF + 90° = 126°
( °.° EF_|_ CD .°. <FED=90°
=> <GEF = 126°-90°=36°
(3) <GEC+<GEF+<FED= 180°
=> <GEC+36°+90°= 180°
=> <GEC=180°-126°=54°
now,
<FGE=<GEC= 54° ( alternate angle)