Question

Question 3
In the given figure, if $AB||DE,\angle BAC={35}^{\circ }and\angle CDE={53}^{\circ },find\angle DCE.$

Answer 1

$AB||DE$ and $AE$ is a transversal.
$\angle BAC=\angle CED$ (Alternate interior angles)
$\therefore \angle CED={35}^{\circ }$
In $\Delta CDE,$
$\angle CDE+\angle CED+\angle DCE={180}^{\circ }$ ( Angle sum property of a triangle)
${53}^{\circ }+{35}^{\circ }+\angle DCE={180}^{\circ }$
$\angle DCE={180}^{\circ }-{88}^{\circ }$
$\angle DCE={92}^{\circ }$