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