Question

In the given figure, LM = LN = 46°. Express x in terms of a, b and c where a, b, c are lengths of LM, MN and NK respectively.

Answer 1

Given: In the given figure

TO EXPRESS: x in terms of a, b, c where a, b, and c are the lengths of LM, MN and NK respectively.

Here we can see that. It forms a pair of corresponding angles.

Hence, LM || PN

In $∆\mathrm{LMK}$ and $∆\mathrm{PNK}$,

$$\begin{gathered} \angle \mathrm{LMK}=\angle \mathrm{PNK}\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle \mathrm{LKM}=\angle \mathrm{PKN}\left(\mathrm{Common}\right) \\ \therefore ∆\mathrm{LMK}~∆\mathrm{PNK}\left(\mathrm{AA}\mathrm{Similarity}\right) \end{gathered}$$

$$\begin{gathered} \frac{\mathrm{ML}}{\mathrm{NP}}=\frac{\mathrm{MK}}{\mathrm{NK}} \\ \frac{a}{x}=\frac{b+c}{c} \\ x=\frac{ac}{b+c} \end{gathered}$$

Hence we got the result as .