In the given figure, AB || CD. Find the angles x, y and z.

From figure,

∠ECF = 90°, ∠CEF = 30°, ∠AFD = 80°

In △ECF, the sum of interior angles is 180°.

∴ ∠ECF + ∠CEF + ∠EFC = 180°

⇒ 90° + 30° + x° = 180°

⇒ 120° + x° = 180°

⇒ x° = 180° - 120°

⇒ x° = 60°

Consider, AB || CD:

z° and 80° are co-interior angles.

Co-interior angles are supplementary:

∴ z° + 80° = 180°

⇒ z° = 180° - 80°

⇒ z° = 100°

Since CD is a straight line, the sum of all angles on one side of a straight line at a point is 180°.

∴ x° + y° + 80° = 180°

⇒ 60° + y° + 80° = 180°

⇒ y° + 140° = 180°

⇒ y° = 180° - 140°

⇒ y° = 40°

x° = 60°, y° = 40° and z° = 100°