Question

In the fig., ∠M = ∠N = 46°, Express x in terms of a, b and c.

Answer 1

Two Triangles are said to be similar if their
i) corresponding angles are equal and
ii) corresponding sides are proportional.(the ratio between the lengths of corresponding sides are equal)

SOLUTION :

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)

HOPE THIS WILL HELP YOU...

Answer 2

In triangle KML and triangle KNP,
angle M=angle N
angle K=angle K
Hence, triangle KML is similar to triangle KNP
Hence,PN/LM=KN/KM
k/a=c/b+c
k=ac/b+c