Question

In Fig. 6.30, if AB II CD. EF I CD and
GED=126", find Z AGE, Z GEF and ZFGE.​

Answer 1

Step-by-step explanation:

GEF + ∠FEG = ∠GED

EF ⊥ CD so that ∠ FED = 90°

And given that ∠ GED = 126°

Plug the values we get

∠GEF + 90° = 126°

∠GEF = 126°- 90°

∠GEF = 36°

AB || CD, EF ⊥ CD so ∠EFG = 90°

Use angle sum property of triangle (sum is 180°)

∠GEF + ∠EFG + ∠FGE = 180°

Plug the values we get

36° + 90° + ∠FGE = 180°

∠FGE = 180° – 36° - 90°

∠FGE = 54°

AB is a straight line so that use linear pair property

∠AGE +∠FGE = 180°

Plug the value of ∠FGE = 54°

We get

∠AGE +54° = 180°

∠AGE = 180° - 54°

∠AGE = 126°