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Offline Centres

In the given figure, $AE = BC$ and $AE | | BC$ and the three sides $AB, CD$ and $ED$ are equal in length. If $∠ A = 102^{\circ} .$ Find the measure of $∠ BCD$ .

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138^{\circ}

162^{\circ}

88^{\circ}

None of these

answer is B.

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Detailed Solution

Given that

AE = BC

AE | | BC

and

AB = CD =

ED

Also

∠ A = 102^{\circ}

.
To

f

ind measure of

∠ BCD .

So if a line will be drawn parallel to

AB

from

E

, the line

EC

will be passed through

C

and

AB = EC

.
And parallelogram will be formed.
And in parallelogram opposite angles are equal.
So,

∠ BAE = ∠ BCE = 102^{\circ}

And AB = EC = CD = ED
So, ECD is equilateral triangle and all the three angleS will be equal.

∠ ECD = 60^{\circ}

So,

∠ BCD = ∠ BCE + ∠ ECD = 102^{\circ} + 60^{\circ} = 162^{\circ}

\Rightarrow ∠ BCD = 102^{\circ} + 60^{\circ}

\Rightarrow ∠ BCD = 162^{\circ}

The measure of

∠ BCD = 162^{\circ}

.
Therefore option 2 is correct.

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