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Sum of Angles of a Quadrilateral

In the given ...

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

120°

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140°

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150°

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160°

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Solution

The correct option is D
160°

Solution: Join CE

A

ABCE is a parallelogram (one pair of opposite sides are equal and parallel)

Therefore, AB = CE =CD = DE ….. (i)

CDE is equilateral …… (from (i)

Thus $∠ E C D = 60^{\circ}$

$∠ B C E = ∠ B A E = 100^{\circ}$ ….. (opposite angles of a parallelogram)

Thus, $∠ A C D = ∠ A C E + ∠ E C D$

$= 100^{\circ} + 60^{\circ}$

$= 160^{\circ}$

Hence (D)

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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