In the given figure, AB || CD || EF and AD || BE. Find x, y and z.

Consider AB || CD and AD is a transversal:

y° = 115° $\quad$[Alternate angles]

∠BAD and ∠ABE are co-interior angles.

Since, line GB intersects at point B, therefore ∠ABE = (x° + 30°)

Co-interior angles are supplementary:

∴ ∠BAD + ∠ABE = 180°

⇒ 115° + x° + 30° = 180° $\quad$[Substituting the value of ∠ABE]

⇒ x° + 145° = 180°

⇒ x° = 180° - 145°

⇒ x° = 35°

Now, consider AB || EF and BE is a transversal:

∠BEF = ∠ABE $\quad$[Alternate angles]

⇒ ∠BEF = x° + 30° $\quad$[Substituting the value of ∠ABE]

⇒ ∠BEF = 35° + 30° $\quad$[Substituting the value of x]

⇒ ∠BEF = 65°

∴ z° = 65°

x° = 35°, y° = 115° and z° = 65°