Question

In the given figure, $AB\Vert CD,\angle EAB=30^{\circ }$ and $\angle EDC=40^{\circ }$. Then the measure of $\angle DEA$ is_____

Answer 1

Answer: 70

Given $AB\Vert CD$
Draw a line (l) passing through E, parallel to $AB$.
Let us say $l$ meets $AD$ at $P$.
$\therefore AB\Vert l\Rightarrow CD\Vert I$
$\angle AEP=\angle EDC=40^{\circ }\text{ ( }\because \text{ Alternate angles) }$
$\angle PEA=\angle EAB=30^{\circ }\text{ ( }\because \text{ Alternate angles) }$
$\therefore \angle DEA=\angle DEP+\angle PEA=40^{\circ }+30^{\circ }$
$\angle DEA=70^{\circ }$