Question

Q10. AB∥CD and CD∥EF. Also EA⊥AB. If ∠BEF = 55⁰, find the value of x, y and z.

OR
If AB║CD, EF⊥CD and ∠GED =126⁰, find ∠AGE, ∠GEF and ∠FGE in the figure given below:

Answer 1

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

Solution :

∠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°