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Question
In the given figure, AE and BC are equal and parallel. If the sides AB, CD and DE are equal and ∠BAE = 100°, then ∠AED is equal to
In the given figure, AE and BC are equal and parallel. If the sides AB, CD and DE are equal and ∠BAE = 100°, then ∠AED is equal to
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Solution
The correct option is B 140°
Join CE 
ABCE is a parallelogram (one pair of opposite sides are equal and parallel)
Therefore, AB = CE =CD = DE ….. (i)
CDEis equilateral …… (from (i)
Thus ∠DEC =60°
∠AEC = 180° - 100° ….. (adjacent angles of a parallelogram)
= 80°
Thus, ∠AED = ∠AEC + ∠DEC
= 80° + 60°
= 140°
Hence (B)
140°
Join CE
ABCE is a parallelogram (one pair of opposite sides are equal and parallel)
Therefore, AB = CE =CD = DE ….. (i)
CDEis equilateral …… (from (i)
Thus ∠DEC =60°
∠AEC = 180° - 100° ….. (adjacent angles of a parallelogram)
= 80°
Thus, ∠AED = ∠AEC + ∠DEC
= 80° + 60°
= 140°
Hence (B)
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