In given figure, PQ, RS and UT are parallel lines.

(i) If c = 57° and a = c/3, find the value of d.

(ii) If c = 75° and a = 2/5 c, find

(i) We have ∠c = 57° and ∠a =  (∠c)/3

∠a = 573 = 19°

PQ || UT (given)

∠a + ∠b = ∠c (Alternate interior angles)

19° + ∠b = 57°

∠b = 57° – 19° = 38°

PQ || RS (given)

∠b + ∠d = 180° (Co-interior angles)

38° + ∠d = 180°

∠d = 180° – 38° = 142°

Thus, ∠d = 142°

(ii) We have ∠c = 75° and ∠a =2/5∠c

∠a =2/5× 75° = 30°

PQ || UT (given)

∠a + ∠b = ∠c

30° + ∠b = 75°

∠b = 75° – 30° = 45°

Thus, ∠b = 45°