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प्रश्न
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.
उत्तर
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
\[\angle LKM = \angle PKN \left( \text{Common} \right)\]
\[ \therefore ∆ LMK~ ∆ PNK \left( \text{AA Similarity} \right)\]
\[\frac{a}{x} = \frac{b + c}{c}\]
\[x = \frac{ac}{b + c}\]
Hence we got the result as \[x = \frac{ac}{b + c}\].
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