Question

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

Answer 1

Answer:

The value of x in terms of a, b and c is ac/(b+c)

Step-by-step explanation:

GIVEN:  

∠KNP = ∠ KML = 46° ,LM = a , MN = b , NK = c

In  ∆KPN  and ∆KLM,  

∠ KNP = ∠KML = 46°    [ given]

∠ K =  ∠ K     [Common]  

∆KPN  ~ ∆KLM   [by AA similarity criterion  of triangles]

KN/ KM = NP/ML  

[corresponding sides of similar triangles are proportional]

c /(b+c) = x/a      [KM = MN + NK]

x(b+c) = c×a      

x = ac/ (b+c)

Hence, the value of x = ac/(b+c)

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