(i) ∠ABC = ∠Y = 100° [In a parallelogram opposite angles are equal]

∠x + ∠Y = 180° [In a parallelogram sum of the adjacent angles is equal to 180°]

∠x + 100° = 180°

∠x = 180°-100°

∠x = 80°

∠x = ∠z = 80° [In a parallelogram opposite angles are equal]

(ii) ∠PSR + ∠Y = 180° [In a parallelogram sum of the adjacent angles is equal to 180°]

∠Y + 50° = 180°

∠Y = 180°- 50°

∠Y = 130°

∠x = ∠Y = 130° [In a parallelogram opposite angles are equal]

∠PSR = ∠PQR = 50° [In a parallelogram opposite angles are equal]

∠PQR + ∠Z = 180° [Linear pair]

50° + ∠Z = 180°

∠Z = 180°-50°

∠Z = 130°

(iii) In ΔPMN

∠MPN + ∠PMN + ∠PNM = 180° [Sum of all the angles of a triangle is 180°]

30° + 90° + ∠z = 180°

∠z = 180°-120°

∠z = 60°

∠y = ∠z = 60° [In a parallelogram opposite angles are equal]

∠z = 180°- 120° [In a parallelogram sum of the adjacent angles is equal to 180°]

∠z = 60°

∠z + ∠NML = 180° [In a parallelogram sum of the adjacent angles is equal to 180°]

60° + 90°+ ∠x = 180°

∠x = 180°-150°

∠x = 30°

(iv) ∠x = 90° [vertically opposite angles are equal]

In ΔDOC

∠x + ∠y + 30° = 180° [Sum of all the angles of a triangle is 180°]

90° + 30° + ∠y = 180°

∠y = 180°-120°

∠y = 60°

∠y = ∠z = 60° [alternate interior angles are equal]

(v) ∠x + ∠POR = 180° [In a parallelogram sum of the adjacent angles is equal to 180°]

∠x + 80° = 180°

∠x = 180°- 80°

∠x = 100°

∠y = 80° [In a parallelogram opposite angles are equal]

∠QRS =∠x = 100°

∠QRS + ∠Z = 180° [Linear pair]

100° + ∠Z = 180°

∠Z = 180°-100°

∠Z = 80°

(vi) ∠y = 112° [In a parallelogram opposite angles are equal]

∠y + ∠TUV = 180° [In a parallelogram sum of the adjacent angles is equal to 180°]

∠z + 40° + 112° = 180°

∠z = 180°- 152°

∠z = 28°

∠z =∠x = 28° [alternate interior angles are equal]