Question

In the adjoining figure, ABCD is a
quadrilateral in which $\left[AD\parallel BC\right]$ and $\left[AB\parallel DC\right]$ Prove that $[\angle ADC=\angle ABC]$

Answer 1

Consider the given that, $ABCD$ is a quadrilateral.

And $AD\parallel BC$ then,

$\angle CDA+\angle DAB={180}^0......\left(1\right)$ (Interior is of transversal AD)

$\angle DAB+\angle ABC={180}^0......\left(2\right)$ Same reason

By equation (1) and (2) to and we get,

$\angle CDA+\angle DAB=\angle DAB+\angle ABC$

$\Rightarrow \angle CDA=\angle ABC$

$\angle ABC=\angle CDA$

Hence proved.