Question

3. In Fig. 6.30, if AB || CD, EF perpendicular to CD and
.angle GED = 126”, find angle AGE, angle GEF and angle FGE. .​

Answer 1

Answer:

∠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°