Question

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

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°

∠GEF=36°

(iii) ∠CEG+∠GED=180°

(GIVEN ∠GED=126∘)

∠CEG+126° =180°

∠CEG=180° −126°

∠CEG=54°

∠FGE=∠CEG= 54°     (alternate angles)

HOPE THIS WILL HELP YOU...

Answer 2

Hi ,

It is given that EF perpendicular to CD ,

<GED = 126°

<FED = 90° and

<GEF = <GED - <FED

<GEF = 126° - 90° = 36°

In ∆ GFE

<GEF + <FGE + <EFG = 180°

36° + <FGE + 90° = 180°

<FGE = 180° - 126° = 54°

<AGE = <GFE + <GEF

[ Since , exterior angle in ∆GFE ]

= 90° + 36°

= 126°

I hope this helps you.

: )