Question

In the fig. If AB || CD, EF ⊥ CD and ∠GED=1260, find ∠AGE,∠GEF and ∠FGE.

Answer 1

Given :AB∥CD

EF⊥CD

⇒∠FED=90∘

Given:∠GED=126∘

⇒∠GEF=∠GED−∠FED=126∘−90∘

∴∠GEF=36∘

In △FGE,∠GFE+∠GEF+∠EGF=180∘ by angle sum property.

⇒90∘+36∘+∠EGF=180∘

⇒∠EGF=180∘−126∘=66∘

∠AGE=∠AGF-∠EGF

⇒∠AGE=180∘−66∘=114∘

∴∠AGE=114∘,∠GEF=36∘ and ∠FGE=66∘