In the given figure, AB || DC and BC || AD. Find the values of x, y and z.

From the figure,

∠ABC = 110°, ∠BCD = x°, ∠ADC = z°, ∠DCE = y°

Since AB || CD and BC || AD, the figure ABCD is a parallelogram.

Consider parallel lines AB and CD with BC acting as a transversal.

Angles ∠ABC and ∠BCD are co-interior angles.

Co-interior angles are supplementary:

∴ ∠ABC + ∠BCD = 180°

⇒ 110° + x° = 180° $\quad$ [Substituting the values of ∠ABC and ∠BCD]

⇒ x° = 180° - 110°

⇒ x° = 70°

Angles ∠BCD (x°) and ∠DCE (y°) form a linear pair. So, they must sum to 180°.

∴ ∠BCD + ∠DCE = 180°

⇒ 70° + y° = 180° $\quad$ [Substituting the values of ∠BCD and ∠DCE]

⇒ y° = 180° - 70°

⇒ y° = 110°

In a parallelogram, opposite angles are equal.

Angle z° is opposite to ∠ABC

∴ z° = ∠ABC

z° = 110° $\quad$ [Substituting the values of ∠ABC]

x° = 70°, y° = 110° and z° = 110°