In Fig. 6.30, if AB || CD, EF ⊥ CD and ∠ GED = 126°, find ∠ AGE, ∠ GEF and ∠ FGE.

Given that: AB||CD,
Therefore,
∠AGE = ∠GED [∵ Alternater Angles]
⇒ ∠AGE = 126°
From the figure,
∠GED = ∠GEF + ∠FED
⇒ 126° = ∠GEF + 90°
⇒ ∠GEF = 126° – 90° = 36°
Given that: AB||CD,
Therefore,
∠FGE + 126° = 180° [∵ Sum of co-interior angles]
⇒ ∠FGE = 180° – 126° = 54°