Question

In fig 6.30, if AB||CD, EF perpendicular CD and angle ged =126°, find angle age, angle gef, angle fge

Answer 1

Answer:

Step-by-step explanation:

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)