Question

In figure, express x in terms of a,b and c.

Answer 1

In $△KPNand△KLM$, we have
$\angle KNP=\angle KML={46}^o$ [Given]
$\angle K=\angle K$ [Common]
$\therefore △KNP\sim △KML$
[By AA-criterion of similarity]
$\Rightarrow \frac{KN}{KM}=\frac{NP}{ML}$ [$\therefore$ Corresponding sides of similar triangles are proportional]
$\Rightarrow \frac{c}{b+c}=\frac{x}{a}\Rightarrow x=\frac{ac}{b+c}$