Question

In the given figure,

AE and BC are equal and parallel. If the sides AB, CD and DE are equal and $\angle$BAE = 100°, then $\angle$BCD is equal to .

• A. 120°
• B. 100°
• C. 160°
• D. 60°

Answer 1

The correct option is C 160°

In the given figure, join CE

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 $\angle$ECD =60°
Given, $\angle$EAB = 100°.
$\angle$EAB = $\angle$BCE (opposite angles in a parallelogram are equal.)
$\angle$BCE = 100°

Thus, $\angle$BCD = $\angle$BCE + $\angle$ECD
= 100° + 60°
​​​= 160°.
Hence, the value of $\angle$BCD is 160°.