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, ∠BAR = 63°, ∠CAS = 57°

AB is its transversal.

∴ ∠CBA = ∠BAR     (Alternate angles)

⇒ a = 63°

∵ PQ || RS and CA is its transversal

∴ ∠QCA + ∠CAS = 180°   (Co-interior angles)

⇒ b + 57° = 180°

⇒ b = 180° - 57° = 123°

But ∠CAS + ∠CAB + ∠BAR = 180°   (Straight line angles)

∴ 57° + c + 63° = 180°

⇒ c + 120° = 180°

⇒ c = 180° - 120° = 60°

Hence a = 63°, b = 123°, c = 60°