Question

In the figure given above, $AB$ is parallel to $CD$. If $\angle BAF={98}^{\circ }$ and $\angle ABC={144}^{\circ }$, then what is $\angle ECD$ equal to?

• A. ${62}^{\circ }$
• B. ${64}^{\circ }$
• C. ${82}^{\circ }$
• D. ${84}^{\circ }$

Answer 1

The correct option is A ${62}^{\circ }$

Draw $l\parallel AB$ through $F$.
$AB\parallel l\Rightarrow {98}^{\circ }+\angle AFP={180}^{\circ }$
$\angle AFP={82}^{\circ }$
$\angle CFP={144}^{\circ }-{82}^{\circ }={62}^{\circ }$
$\angle ECD=\angle CFP$ ....(corresponding angles)
Therefore, $\angle ECD={62}^{\circ }$