Question

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

• A. ${138}^{\circ }$
• B. ${162}^{\circ }$
• C. ${88}^{\circ }$
• D. None of these

Answer 1

Answer: (B)

${162}^{\circ }$

As $AE = BC$and$AE || BC$Soifalinewillbedrawnparallelto$AB$from$E$,theline$EC$willbepassthrough$C$and$AB=EC$
And parallelogram will be formed.
and in parallelogram opposite angels are congruent.
So,
$\angle BAE=\angle BCE={102}^{\circ }$
And AB=EC=CD=ED
So, ECD is equilateral triangle and all the three angle will be equal.
$\angle ECD={60}^{\circ }$
So, $\angle BCD=\angle BCE+\angle ECD={102}^{\circ }+{60}^{\circ }={162}^{\circ }$
Answer - option $B$ is correct