Question

In given figure $AB\parallel DC$. Find the value of $x$ .

Answer 1

REF.Image.

Here $\Delta AOB$ is similar

to $\Delta COD$

because

$\angle CDO=\angle OBA$

$\angle DCO=\angle OAB$

Alternate interior angle an equal in $\parallel$ lines

$\angle DOC=\angle AOB$ (opposite angles are equal)

So its similar by (AAA)

(Angle Angle Angle ) criteria.

So $\Delta AOB\sim \Delta COD$

$\Rightarrow \frac{AO}{CO}=\frac{BO}{DO}$

from similatrily properly

$\frac{x+5}{x+3}=\frac{x-1}{x-2}$

$(x+5)(x-2)=(x-1)(x+3)$

$x^2-2x+5x-10=x^2-x+3x-3$

$3x-10=2x-3$

$x=7$