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  ∠ LMN = ∠ PNK= `46^o` 

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. ∠ LMN = ∠ PNK= `46^o` It forms a pair of corresponding angles.

Hence, LM || PN

In 

\[∆ LMK\] and \[∆ PNK\]

\[\angle LMK = \angle PNK \left( \text{Corresponding angles} \right)\]
\[\angle LKM = \angle PKN \left( \text{Common} \right)\]
\[ \therefore ∆ LMK~ ∆ PNK \left( \text{AA Similarity} \right)\]

\[\frac{ML}{NP} = \frac{MK}{NK}\]
\[\frac{a}{x} = \frac{b + c}{c}\]
\[x = \frac{ac}{b + c}\]

Hence we got the result as \[x = \frac{ac}{b + c}\].