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In the given figure AE = BC and AE || BC and the three sides AB, CD and ED are equal in length. If ∠A = 102°, then find the measure of ∠BCD.(a) 138° (b) 162° (c) 88° (d) 150° |
Answer» (b) 162°. AE || BC and AE = BC ⇒ AECB is a parallelogram. (For a parallelogram one pair of opposite sides can be shown equal and parallel) ∴ ∠BCE = ∠BAE = 102° (Opposite angles of a parallelogram are equal) AB = EC (Opposite sides of a parallelogram) ED = CD = EC (∵ AB = ED = CD) ∴ ∆EDC is equilateral ⇒ ∠ECD = 60° ∴ ∠BCD = ∠BAE + ∠ECD = 102° + 60° = 162°. |
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