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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 ∠BCD 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 ∠BCD is equal to
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Solution
The correct option is D 160°
Solution: Join CE
A
Since AE and BC are parallel and equal if we join CE then it will be parallel and equal to AB. Hence ABCE is a parallelogram.
Therefore, AB = CE =CD = DE ….. (i)
CDE is equilateral …… (from (i))
Thus ∠ECD =60°
Given, ∠EAB = 100°.
∠EAB = ∠BCE (opposite angles in a parallelogram are equal.)
= 100°
Thus, ∠BCD = ∠BCE + ∠ECD
= 100° + 60°
= 160°
160°
Solution: Join CE
A
Since AE and BC are parallel and equal if we join CE then it will be parallel and equal to AB. Hence ABCE is a parallelogram.
Therefore, AB = CE =CD = DE ….. (i)
CDE is equilateral …… (from (i))
Thus ∠ECD =60°
Given, ∠EAB = 100°.
∠EAB = ∠BCE (opposite angles in a parallelogram are equal.)
= 100°
Thus, ∠BCD = ∠BCE + ∠ECD
= 100° + 60°
= 160°
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