Question

in the given figure, angle M = angle N = 46 degree . Express x in terms of a,b and c , where a,b and c lengths of LM and MN and NK respectively.
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Answer 1

Given : angle M = angle N = 46 degree . a,b and c lengths of LM and MN and NK respectively.

To Find : Express x in terms of a,b and c

Solution:

comparing ΔLMK  & ΔPNK

∠M = ∠N = 46°

∠K = ∠K   ( common)

∠L = ∠P  ( if two angles are equal then third angle will also be equal )

=>  ΔLMK  ≈ ΔPNK

=> LM/PN  =  MK/NK

LM = a

MK = MN + NK = b + c

NK = c

PN = x

=> a/x  = (b+ c)/c

=> x = ac/(b + c)

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

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