Question

In the given figure, find the value of x, if $AB||CD.$

• A. $3$ m
• B. $4$ m
• C. $8$ m
• D. $2$ m

Answer 1

The correct option is A $3$ m

$AB\parallel CD,CB$ is transversal
$\therefore \angle OBA=\angle OCD$ (corresponding angles)
$\therefore \angle OAB=\angle ODC$ (corresponding angles are equal)
$△OAB$ & $△ODC$
$\angle BOA=\angle COD$ (common angle)
$\angle OBA=\angle OCD$
$\therefore$ By AA corollary
$△OAB\sim △ODC$
$\therefore \frac{AB}{DC}=\frac{OA}{OD}$$\Rightarrow \frac{1.83}{5.49}=\frac{x}{6+x}\Rightarrow x=3m$