Fig. 3.29In Fig. 3.30, if AB II CD, EF 1 CD andGED- 126Â°, find Z AG

1.	Fig. 3.29In Fig. 3.30, if AB II CD, EF 1 CD andGED- 126Â°, find Z AGE, GEF and FGE.3.A G
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 thatEF⊥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)

Fig. 3.29In Fig. 3.30, if AB II CD, EF 1 CD andGED- 126Â°, find Z AGE, GEF and FGE.3.A G

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 thatEF⊥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)