Question

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

Answer 1

In $△KPN$ and $△KLM$, we have

$\angle KNP=\angle KML={46}^{\circ }$ [Given]

$\angle K=\angle K$ [Common]

$\therefore$ $△KNP\sim △KML$ [By AA-criterion of similarity]

$\Rightarrow$ $\frac{KN}{KM}=\frac{NP}{ML}$ [$\because$ Corresponding sides of similar triangles are proportional]

$\Rightarrow$ $\frac{c}{b+c}=\frac{x}{a}$

$\Rightarrow x=\frac{ac}{b+c}$