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 $\angle$AED is equal to

• A. 120°
• B. 140°
• C. 150°
• D. 160°

Answer 1

The correct option is B

140°

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 $\angle$DEC =60°

In parallelogram ABCE

$\angle$EAB + $\angle$AEC = 180${}^{\circ }$ (adjacent angles are supplementary in a parallelogram)

$\angle$AEC = 180° - 100°

= 80°

Thus, $\angle$AED = $\angle$AEC + $\angle$DEC

= 80° + 60°

= 140°