Question

If $ABIIDE,\angle BAC={35}^{\circ }$ and $\angle CDE={53}^{\circ },$ find $\angle DCE$

Answer 1

As $AB||DE$

$\angle BAE=\angle AED=\angle CED={35}^{\circ }$ (Alternate interior angles)

$\angle CDE={53}^{\circ }$ (Given)

$\angle CDE+\angle DEC+\angle ECD={180}^{\circ }$

${53}^{\circ }+\angle CED+\angle ECD={180}^{\circ }$

${53}^{\circ }+{35}^{\circ }+\angle DCE={180}^{\circ }$

$\angle DCE={180}^{\circ }-{53}^{\circ }-{35}^{\circ }$

$\angle DCE={92}^{\circ }$