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

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» <p>Alternate angles:When two lines are crossed by another line the pair of angles on opposite sides of the transversal is called alternate angles.</p><p>Theorem 1:If a transversal intersects two Parallel Lines then each pair of alternate interior angles is equal.</p><p>Theorem 2 :If a transversal intersects two lines such that a pair alternate interior angle is equal then the two lines are parallel.</p><p>SOLUTION:</p><p>Given: ∠AGE=126°</p><p>∠AGE=∠GED=126∘[alternate interior angles]</p><p>(ii)∠GED=∠GEF+∠FED=126∘</p><p>∠GEF + 90° =126°</p><p>(GIVEN thatEF⊥CD)</p><p>∠GEF=126°−90°=36°</p><p>∠GEF=36°</p><p>(iii)∠CEG+∠GED=180°</p><p>(GIVEN ∠GED=126∘)</p><p>∠CEG+126° =180°</p><p>∠CEG=180° −126°</p><p>∠CEG=54°</p><p>∠FGE=∠CEG= 54°(alternate angles)</p>