1.

In the adjacent figure AB||CD,EF/CD and ∠GED=126°, find ∠AGE, ∠GEF and ∠FGE.

Answer»

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°

∠GEF=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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