Question

In the given figure,find the value of x in terms of a,b and c

Answer 1

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Answer 2

Prove first set of angles is the same:

∠LMN = 50º (Given)

∠PNK = 50º (Given)

⇒ ∠LMN  = ∠PNK  (Same Angle Values)

⇒ KN // PN

Prove second set of angles is the same:

∠LKM = ∠PKN (Common Angles)

Prove third set of angles is the same:

Since KN // PN and LPK is a straight line

∠MPK = ∠PNK (Same Angle Values)

By property of AAA, the two angles are similar

⇒ LM/PN = MK/NK

⇒ a/x = (b + c)/c

Make x the subject:

a/x = (b + c)/c

x(b + c) = ac

x = ac/(b + c)

Answer: x =  ac/(b + c)