Question

In the following figures, PQ is parallel to RS. Find the angles a, b and c:

Answer 1

In the given figure,

PQ || RS, ∠B = 75°, ∠ACS = 140°

AB is its transversal

∴ ∠PAB = ∠ABC

⇒ a = 75°

Again PQ || RS and AC is its transversal

∴ ∠QAC + ∠ACS = 180°   (Co-interior angles)

⇒ c + 140° = 180°

⇒ c = 180° - 140° = 40°

But a + b + c = 180°   (Straight line angles)

∴ 75° + b + 40° = 180°

⇒ b + 115° = 180°

⇒ b = 180° - 115° = 65°

Hence a = 75°, b = 65°, c = 40°