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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, ∠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°
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