Question

In the following figure, $AE$ and $BC$ are equal and parallel and the three sides $AB$, $CD$ and $DE$ are equal to one another. If angle $A$ is ${102}^0$. Find angles $AEC$ and $BCD$.

• A. ${62}^{\circ },{140}^{\circ }$
  
• B. ${78}^{\circ },{162}^{\circ }$
• C. ${78}^{\circ },{142}^{\circ }$
• D. None of these

Answer 1

The correct option is B ${78}^{\circ },{162}^{\circ }$

if we will draw line between $E$ and $C$ i.e. $EC$, then it will be equal and parallel to $AB$.

So, $ECD$ will be equilateral triangle and angle will be ${60}^o$.

and $ABCE$ will be parallelogram, where $AE$ and $BC$ are equal and parallel and $AB$ and $EC$ are equal and parallel.

angle $AEC$ $=180°-102°=78°$

$\angle BCD=\angle BCE+\angle ECD=102°+60°=162°$