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Question
In the following figure, BA is parallel to CD. Find the angles a, b and c:
Solution
In the given figure,
ABC is a triangle and CD || BA, BC is produced to E.
∠A = 60°, ∠B = 70°
∵ AB || DC and BE is its transversal
∴ ∠DCE = ∠ABC (Corresponding angles)
⇒ a = 70°
∴ a = 70°
Similarly, AB || DC and AC is its transversal
∴ ∠ACD = ∠BAC (Alternate angles)
⇒ b = 60°
∴ b = 60°
But a + b + c = 180° (Straight line angle)
⇒ 70° + 60° + c = 180°
⇒ 130° + c = 180°
⇒ c = 180° - 130° = 50°
Hence a = 70°, b = 60° and c = 50°
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