Question

In figure, if $AB\parallel DE,\angle BAC={35}^o$ and $\angle CDE={53}^o$, find $\angle DCE$.

• A. ${102}^o$
• B. ${92}^o$
• C. ${82}^o$
• D. ${72}^o$

Answer 1

The correct option is B ${92}^o$

$AB\parallel DE$, $AE$ is transversal\

$\Rightarrow \angle BAC=\angle CED$ .....(Alternate interior angles)\\

$\Rightarrow \angle CED=35$

In $△CDE$ using angle sum property of triangle.

$\angle CDE+\angle DCE+\angle CED=180$

$\Rightarrow 53+\angle DCE+35=180$

$\Rightarrow \angle DCE=180+88=92$

Hence, $\angle DCE=92$