Question

In fig if $AB$ $\parallel$ $DE$, $\angle BAC={35}^{\circ }$ and $\angle CDE={53}^{\circ }$, find $\angle DCE$ in degrees.

Answer 1

Given, $AB\parallel DE$,
$\angle BAC=\angle CED={35}^{\circ }$ (Alternate angles of parallel lines AB and DE)
In $△CDE$,
$\angle CDE+\angle DCE+\angle CED=180$
$53+35+\angle DCE=180$
$\angle DCE=180-88$
$\angle DCE={92}^{\circ }$